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author | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
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committer | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
commit | e0c6872cf40896c7be36b11dcc744620f10adf1d (patch) | |
tree | 60335e10d2f4354b0674ec22d7b53f0f8abee672 /macros/latex/contrib/utthesis/ICDE-11 |
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diff --git a/macros/latex/contrib/utthesis/ICDE-11/abstract.tex b/macros/latex/contrib/utthesis/ICDE-11/abstract.tex new file mode 100644 index 0000000000..c966ccb075 --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/abstract.tex @@ -0,0 +1,23 @@ +\firstpage +\begin{abstract} +{\itshape +From our experience, current rule-based query optimizers do not provide +a very intuitive and well-defined framework to define rules and +actions. To remedy this situation, we propose an extensible and +structured algebraic framework called Prairie for specifying rules. +Prairie facilitates rule-writing by enabling a user to write rules and +actions more quickly, correctly and in an easy-to-understand and +easy-to-debug manner. + +Query optimizers consist of three major parts: a search space, a cost +model and a search strategy. The approach we take is only to develop +the algebra which defines the search space and the cost model and use +the Volcano optimizer-generator as our search engine. Using Prairie as +a front-end, we translate Prairie rules to Volcano to validate our +claim that Prairie makes it easier to write rules. + +We describe our algebra and present experimental results which +show that using a high-level framework like Prairie to design +large-scale optimizers does not sacrifice efficiency. +} +\end{abstract} diff --git a/macros/latex/contrib/utthesis/ICDE-11/conclusion.tex b/macros/latex/contrib/utthesis/ICDE-11/conclusion.tex new file mode 100644 index 0000000000..fbfb02c0c5 --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/conclusion.tex @@ -0,0 +1,49 @@ +\section{Conclusion and future work} +\label{sec:conclusion} + +Current rule-based query optimizers do not provide a very intuitive and +conceptually streamlined framework to define rules and actions. Our +experiences with the Volcano optimizer generator suggest that its model +of rules and the expression of these rules is much more complicated and +too low-level than it needs to be. As a consequence, rule sets in +Volcano are fragile, hard to write, and debug. Similar problems may +exist in other contemporary rule-based query optimizers. + +We believe that rule-based query optimizers will be standard tools +of future database systems. The pragmatic difficulties of using +existing rule-based optimizers led us to develop Prairie, an +extensible and structured algebraic framework for specifying rules. +Prairie is similar to existing optimizers in that it supports both +transformation rules and implementation rules. However, Prairie +makes several improvements: +\begin{enumerate} +\item it offers a conceptually more streamlined model for rule specification; +\item rules are encapsulated, there are no ``hidden'' operators or + ``hidden'' algorithms; +\item implementation hints (\eg enforcers) are deduced automatically; +\item and it has efficient implementations. +\end{enumerate} + +We have explained how the first three points are important for +simplifying rule specifications and making rule sets less brittle for +extensibility. A consequence is that Prairie rules are simpler and +more robust than rules of existing optimizers (\eg Volcano). We +addressed the fourth point by building a P2V pre-processor which uses +sophisticated algorithms to compose and compact a Prairie rule set into +a Volcano rule set. To demonstrate the scalability of our approach, we +rewrote the TI Open OODB rule set as a Prairie rule set, generated its +Volcano counterpart, and showed that the performance of the synthesized +Volcano rule set closely matches the hand-crafted Volcano rule set. + +Our future work will concentrate on developing higher-level +abstractions using Prairie, including automatically generating Prairie +rule sets, and combining multiple Prairie rule sets to automatically +generate efficient optimizers. + +\section*{Acknowledgments} +\label{sec:acknowledgments} + +We wish to thank Texas Instruments, Inc.\ for making the Open OODB +source code available to us. Comments by Jos\'e Blakeley, Anne Ngu, +Vivek Singhal, Thomas Woo and the anonymous referees greatly improved +the quality of the paper. diff --git a/macros/latex/contrib/utthesis/ICDE-11/eqlogexp.Q1-8.ps b/macros/latex/contrib/utthesis/ICDE-11/eqlogexp.Q1-8.ps new file mode 100644 index 0000000000..6c41dfdf1d --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/eqlogexp.Q1-8.ps @@ -0,0 +1,605 @@ +%!PS-Adobe-2.0 EPSF-1.2 +%%BoundingBox: 18 18 552 482 +%%Creator: ACE/gr (xmgr) v2.10 +%%Title: /u/ddas/research/papers/eqlogexp.Q1-8.ps +%%EndComments +/m {moveto} bind def +/l {lineto} bind def +/RJ { + stringwidth neg exch neg exch + rmoveto +} bind def +/CS { + stringwidth + 2 div neg exch 2 div neg exch + rmoveto +} bind def +0.25 0.25 scale +1 setlinecap +/Times-Italic findfont +72 scalefont + setfont +[] 0 setdash +420 376 m +420 1785 l +2030 1785 l +2030 376 l +420 376 l +stroke +[] 0 setdash +420 376 m +420 396 l +621 376 m +621 396 l +822 376 m +822 396 l +1023 376 m +1023 396 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scalefont + setfont +1110 1414 m +1270 1414 l +stroke +1080 1444 m +1110 1384 l +1140 1444 l +closepath +gsave eofill grestore +stroke +1240 1444 m +1270 1384 l +1300 1444 l +closepath +gsave eofill grestore +stroke +1310 1414 m +gsave +1310 1414 translate +0 rotate +0 -24 m +(Query 7, 8) show +grestore +newpath +showpage +%%Trailer diff --git a/macros/latex/contrib/utthesis/ICDE-11/intro.tex b/macros/latex/contrib/utthesis/ICDE-11/intro.tex new file mode 100644 index 0000000000..b4ebebe580 --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/intro.tex @@ -0,0 +1,82 @@ +\section{Introduction} +\label{sec:intro} + +Query optimization \cite{Grae93} is a fundamental part of database +systems. It is the process of generating an efficient access plan for +a database query. Informally, an access plan is an execution strategy +for a query; it is the sequence of low-level database retrieval +operations that, when executed, produce the database records that +satisfy the query. There are three basic aspects that define and +influence query optimization: the search space, the cost model, and the +search strategy. + +The {\em search space} is the set of logically equivalent access plans +that can be used to evaluate a query. All plans in a query's search +space return the same result; however, some plans are more efficient +than others. The {\em cost model} assigns a cost to each plan in the +search space. The cost of a plan is an estimate of the resources used +when the plan is executed; the lower the cost, the better the plan. +The {\em search strategy} is a specification of which plans in the +search space are to be examined. + +Traditionally, query optimizers have been built as monolithic +subsystems of a DBMS. This simply reflects the fact that traditional +database systems are themselves monolithic: the algorithms used for +storing and retrieving data are hard-wired and are rather difficult to +change. The need to have extensible database systems, and in turn +extensible optimizers, has long been recognized in systems like Genesis +\cite{Bato88a}, EXODUS \cite{Grae87b}, Starburst \cite{Haas88}, and +Postgres \cite{Ston86b}. Rule-based query optimizers are among the +major conceptual advances that have been proposed to deal with query +optimizer extensibility \cite{Haas88,Frey87a,Grae87b,Grae90b}. The +extensibility translates into the ability to incorporate new operators, +algorithms, cost models, or search strategies without changing the +optimization algorithm. + +In this paper, we describe an algebraic framework called \emph{Prairie} +for specifying rules in a rule-based query optimizer. Prairie is +similar to other rule specification languages like Starburst +\cite{Haas88} and Volcano \cite{Grae90b}, and indeed, we have based our +work on Volcano to capture most of the advantages of rule-based +optimizers. However, Prairie attempts to provide some key features +that, we have found, simplify the effort in writing rules: + +\begin{enumerate} + \item A framework in which users can define a query optimizer + concisely in terms of a well-defined set of operators and + algorithms. \emph{All} operators and algorithms are considered + first-class objects, \ie \emph{any} of them can occur in any + rule, and \emph{only} these operators and algorithms can appear + in rules. This scheme eliminates the need for special classes + of operators and algorithms, such as enforcers in Volcano and + glue in Starburst, that significantly complicate rule + specification. + \item A framework in which users can define a list of properties to + characterize the expressions generated in the optimization + process. Again, the goal here is to allow the user to treat + \emph{all} properties as having equal status. This is different + from Volcano where the user must classify properties as logical, + physical, or operator/algorithm arguments. + \item A framework in which users can specify mapping functions + between properties concomitantly with the corresponding rules. + This contrasts with existing approaches in which mappings + between properties are fragmented into multiple functions and at + logically different places than the corresponding rules. + Research into rule-based optimizers has revealed that + property-mapping functions are a major source of user effort, so + this is an important goal. + \item The format (Prairie) in which users can cleanly specify rules is + not necessarily the same format needed for generating efficient + optimizers. Thus, there is a need for a pre-processor (written + by us) that translates between these competing representations. +\end{enumerate} + +Prairie strives for uniformity in dealing with issues that have been a +source of most user effort and potential user errors. In the following +sections, we present the Prairie framework. We explain how our P2V +pre-processor maps Prairie rule specifications into Volcano rule +specifications that can be processed efficiently. Experimental results +to support this claim are given in Section~\ref{sec:results}, where we +compare implementations of the Texas Instruments Open OODB query +optimizer using both Prairie and Volcano. We conclude with a summary +and related research. diff --git a/macros/latex/contrib/utthesis/ICDE-11/model.tex b/macros/latex/contrib/utthesis/ICDE-11/model.tex new file mode 100644 index 0000000000..3a3f916091 --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/model.tex @@ -0,0 +1,831 @@ +\section{Prairie: A language for rule specification} +\label{sec:framework} + +The basic concepts and definitions that underlie the Prairie model are +presented in this section. The goal is to lay a foundation for +reasoning about query optimization algebraically; this is necessary for +our subsequent discussion about translating Prairie specifications to +those of Volcano. + +\subsection {Notation and assumptions} +\label{sec:notation} + +\paragraph{Stored Files and Streams.} +A file is \emph{stored} if its tuples reside on disk. In the case of +relational databases, stored files are sometimes called \emph{base +relations}; we will denote them by $R$ or $R_i$. In object-oriented +schemas, stored files are \emph{classes}; we will denote them by +$\textit{C}$ or $\textit{C}_i$. Henceforth, whenever we refer to a +stored file, we mean a relation or a class; when the distinction is +unimportant, we will use $F$ or $F_i$. A \emph{stream} is a sequence +of tuples and is the result of a computation on one or more streams or +stored files; tuples of streams are returned one at a time, typically +on demand. Streams can be \emph{named}, denoted by $S_i$, or +\emph{unnamed}. + +\paragraph{Database Operations.} +An \emph{operation} is a computation on one or more streams or stored +files. There are two types of database operations in Prairie: +abstract (or implementation-unspecified) operators and concrete +algorithms. Each is detailed below. +\begin{description} % To achieve extra indentation. +\begin{description} +\item[Operators.] +Abstract (or conceptual) \emph{operators} specify computations on +streams or stored files; they are denoted by all capital +letters (\eg JOIN). Operators have two types of parameters: +essential and additional. \emph{Essential parameters} are the stream +or file inputs to an operator; these are the primary inputs to be +processed by an operator. \emph{Additional parameters} are +``fine-grain'' qualifications of an operator; their purpose is to +describe an operator in more detail than essential parameters. + +\item[Algorithms.] +\emph{Algorithms} are concrete implementations of conceptual operators; +they will be represented in lower case with the first letter +capitalized (\eg Nested\_loops). Algorithms have at least the same +essential and additional parameters as the conceptual operators that +they implement.\footnote{Algorithms may have \emph{tuning parameters} +which are not parameters of the operators they implement.} +Furthermore, there can be, and usually are, several algorithms for a +particular operator. +\end{description} +\end{description} +Table~\ref{tab:operators} lists some operators and algorithms implementing +them together with their additional parameters. + +\begin{centeredtable*} +\begin{minipage}[b]{9.9cm} +\nodesizes +\newlength{\first} +\settowidth{\first}{JOIN($S_1$, $S_2$)} +\newlength{\second} +\settowidth{\second}{Join streams $S_1$, $S_2$} +\newlength{\third} +\settowidth{\third}{projected\_attributes} +\newlength{\fourth} +\settowidth{\fourth}{Nested\_loops($S_1$, $S_2$)} +\newlength{\linelength} +\setlength{\linelength}{\fourth+\tabcolsep*2} +\begin{tabular}{|l|l|l|p{\fourth}|} \thickhline +\textbf{Operator} + & \textbf{Description} + & \textbf{Additional Parameters} + & \textbf{Algorithm} \\ \thickhline +\multirow{2}{\first}{JOIN($S_1$, $S_2$)} + & \multirow{2}{\second}{Join streams $S_1$, $S_2$} & tuple\_order + & Nested\_loops($S_1$, $S_2$) \\ \cline{4-4} + & & join\_predicate & Merge\_join($S_1$, $S_2$) \\ \hline +\multirow{3}{\first}{RET($F$)} + & \multirow{3}{\second}{Retrieve file $F$} + & tuple\_order + & \parbox[c][\baselineskip][b]{\fourth}{File\_scan($F$)} \\ + & & selection\_predicate + & \parbox[c]{\linelength} + {\hspace*{-\tabcolsep}\rule{\linelength}{\arrayrulewidth}} \\ + & & projected\_attributes + & \parbox[c][\baselineskip][t]{\fourth}{Index\_scan($F$)} \\ \hline +\multirow{2}{\first}{SORT($S_1$)} + & \multirow{2}{\second}{Sort stream $S_1$} + & \multirow{2}{\third}{tuple\_order} + & Merge\_sort($S_1$) \\ \cline{4-4} + & & & Null($S_1$) \\ \thickhline +\end{tabular} +\caption{Operators and algorithms in a centralized query optimizer and + their additional parameters} +\label{tab:operators} +\end{minipage} +\hfill +\begin{minipage}[b]{6.5cm} +\nodesizes +\settowidth{\first}{projected\_attributes} +\begin{tabular}{|l|l|} \thickhline +\textbf{Property} + & \textbf{Description} \\ \thickhline +join\_predicate + & join predicate for JOIN operator \\ \hline +selection\_predicate + & selection predicate for RET operator \\ \hline +\multirow{2}{\first}{tuple\_order} + & tuple order of resulting stream, \\ + & DONT\_CARE if none \\ \hline +num\_records + & number of tuples of resulting stream \\ \hline +tuple\_size + & size of individual tuple in stream \\ \hline +projected\_attributes + & projected attributes for RET operator \\ \hline +attributes + & list of attributes \\ \hline +cost + & estimated cost of algorithm \\ \thickhline +\end{tabular} +\caption{Properties of nodes in an operator tree} +\label{tab:annotations} +\end{minipage} +\end{centeredtable*} + +\paragraph{Operator Trees.} +An \emph{operator tree} is a rooted tree whose non-leaf, or +\emph{interior}, nodes are database operations (operators or +algorithms) and whose leaf nodes are stored files. The children of an +interior node in an operator tree are the essential parameters (\ie the +stream or file parameters) of the node. Additional parameters are +implicitly attached to each node. Algebraically, operator trees are +compositions of database operations; thus, we will also call operator +trees \emph{expressions}; both terms will be used interchangeably. + +\begin{example} +A simple expression and its operator tree representation are shown +in Figure~\ref{fig:optreeexample}. Relations $R_1$ and $R_2$ are first +RETrieved, then JOINed, and finally SORTed resulting in a stream +sorted on a specific attribute. The figure shows only the essential +parameters of the various operators, not the additional parameters. +\end{example} + +\begin{comment} +The figures which follow. + + SORT + | + | + JOIN + /\ + / \ + RET RET + | | + | | + R1 R2 + + Merge_sort + | + | + Nested_loops + / \ + / \ + File_scan File_scan + | | + | | + R1 R2 + +\end{comment} + +\begin{centeredfigure} +\setlength{\unitlength}{0.6in} +% +\myshadowbox +{ +\subfigure[An expression and its corresponding operator tree] +{ +\begin{centeredinhalfminipage} +\psset{unit=4mm} +\psset{nodesep=1pt} +\tiny +\begin{pspicture}(0,0)(2,4) +\rput(1,4){SORT (JOIN (RET ($R_1$), RET ($R_2$)))} +\rput(1,3){\rnode{sort}{SORT}} +\rput(1,2){\rnode{join}{JOIN}} +\ncline{-}{sort}{join} +\rput(0,1){\rnode{retr1}{RET}} +\rput(2,1){\rnode{retr2}{RET}} +\ncline{-}{join}{retr1} +\ncline{-}{join}{retr2} +\rput(0,0){\rnode{r1}{$R_1$}} +\rput(2,0){\rnode{r2}{$R_2$}} +\ncline{-}{retr1}{r1} +\ncline{-}{retr2}{r2} +\end{pspicture} +\end{centeredinhalfminipage} +\label{fig:optreeexample} +} +% +\vrule +% +\subfigure[Possible access plan for operator tree in (a)] +{ +\begin{centeredinhalfminipage} +\psset{unit=4mm} +\psset{nodesep=1pt} +\tiny +\begin{pspicture}(0,0)(2,3) +\rput(1,3){\rnode{mergesort}{Merge\_sort}} +\rput(1,2){\rnode{nestedloops}{Nested\_loops}} +\ncline{-}{mergesort}{nestedloops} +\rput(0,1){\rnode{filescanr1}{File\_scan}} +\rput(2,1){\rnode{filescanr2}{File\_scan}} +\ncline{-}{nestedloops}{filescanr1} +\ncline{-}{nestedloops}{filescanr2} +\rput(0,0){\rnode{r1}{$R_1$}} +\rput(2,0){\rnode{r2}{$R_2$}} +\ncline{-}{filescanr1}{r1} +\ncline{-}{filescanr2}{r2} +\end{pspicture} +\end{centeredinhalfminipage} +\label{fig:accplanexample} +} +} +% +\caption{Example of an operator tree and access plan} +\label{fig:expexample} +\end{centeredfigure} + +\paragraph{Descriptors.} +A \emph{property} of a node is a (user-defined) variable that contains +information used by an optimizer. An \emph{annotation} is a $\langle +\emph{property, value} \rangle$ pair that is assigned to a node. A +\emph{descriptor} is a list of annotations that describes a node of an +operator tree; every node has its own descriptor. As an example, +Table~\ref{tab:annotations} lists some typical properties that might be +used in a descriptor. Note that descriptors for stream and stored +files may have different properties. The following notations will be +useful in our subsequent discussions. If $S_i$ is a stream, then +$\mathbf{D_i}$ is its descriptor. Annotations of $S_i$ are accessed by +a structure member relationship, \eg +$\mathbf{D_i}.\text{num\_records}$. Also, let $E$ be an expression and +let $\mathbf{D}$ be its descriptor. We will write this as +$E:\mathbf{D}$. + +\begin{example} +The expression, +\begin{eqnarray*} +{\scriptstyle \text{SORT}(\text{JOIN}(\text{RET}(R_1):\mathbf{D_3}, + \text{RET}(R_2):\mathbf{D_4}):\mathbf{D_5}):\mathbf{D_6}} & & +\end{eqnarray*} +corresponds to the operator tree in Figure~\ref{fig:optreeexample}, and +shows the descriptors of the various nodes. +\end{example} + +A notational simplification can be made here. Additional parameters +of operators can be treated the same way as other properties of a node; +essential parameters, however, are \emph{expressions}. Thus, the term +descriptor in the remainder of this paper will refer to a set of properties, +including additional parameters, as shown in Table~\ref{tab:annotations}. + +Currently, descriptor properties are defined entirely by the user; +however, we envision providing a hierarchy of pre-defined descriptor +types to aid this process. + +\paragraph{Access Plans.} +An \emph{access plan} is an operator tree in which all interior nodes +are algorithms. + +\begin{example} +An access plan for the operator tree in Figure~\ref{fig:optreeexample} +is shown in Figure~\ref{fig:accplanexample}. +\end{example} + +\subsection{Prairie optimization paradigm} +\label{sec:topdown} + +Prairie admits two rather different means of optimization: top-down and +bottom-up. A top-down query optimizer optimizes the parents of a node +prior to optimizing the node itself. A bottom-up optimizer optimizes +the children of a node prior to optimizing the node. The earliest +optimizers (System R \cite{Seli79} and R$^*$ \cite{Dani82}) employed +the bottom-up approach. + +Our research concentrates on a top-down optimization of operator +trees. We have chosen this approach because we intend to translate +Prairie rules into the format required by the Volcano query optimizer +generator \cite{Grae90b} which is based on a top-down strategy. +Given an appropriate search engine, Prairie can potentially also be +used with a bottom-up optimization strategy; however, we will not +discuss this approach in this paper. + +In query optimization, there are certain annotations (such as +additional parameters) that are known before any optimization is +begun. These annotations can be computed at the time that the operator +tree is initialized, and will not change with application of rules. +Our following discussions assume operator trees are initialized. + +There are two types of algebraic transformations (or \emph{rewrite +rules}) in Prairie: T-rules (``transformation rules'') and I-rules +(``implementation rules''). Each rule transforms an expression into +another based on additional conditions; the transformation also results +in a mapping of descriptors between expressions. We define T-rules and +I-rules precisely in the following sections and illustrate them with +examples. Our examples are chosen from rules that would be used in a +centralized relational query optimizer; the operators, algorithms, and +properties are subsets of those in Tables~\ref{tab:operators} and +\ref{tab:annotations}. + +\subsection{Transformation rules} +\label{sec:trules} + +\begin{centeredfigure} +\def\subfigtopskip{0pt} +\myshadowbox{ +\begin{tabular}{c} +\subfigure[General form of a T-rule] +{ +\setlength{\topsep}{0pt} +\scriptsize +\begin{minipage}[b]{0.86\linewidth} +\begin{trule} +E(x_1, \ldots, x_n):\mathbf{D_1} \Longrightarrow + E'(x_1, \ldots, x_n):\mathbf{D_2} \label{eq:generaltrule} +\end{trule} +\begin{trulepretest} +\> pre-test statements +\end{trulepretest} +test +\begin{truleposttest} +\> post-test statements +\end{truleposttest} +\end{minipage} +\label{fig:generaltrule} +} \\ \hline +%%% +\subfigure[Join associativity] +{ +\setlength{\topsep}{0pt} +\scriptsize +\begin{minipage}[b]{0.86\linewidth} +\vspace*{4pt} +\begin{trule} +\text{JOIN}(\text{JOIN}(S_1, S_2):\mathbf{D_4}, S_3):\mathbf{D_5} +\label{eq:associativity} +\end{trule} +%%% TODO: Remove extra space above eqnarray. +\begin{eqnarray*} +\rulespace \Longrightarrow + \text{JOIN}(S_1, \text{JOIN}(S_2, S_3):\mathbf{D_6}):\mathbf{D_7} +% \label{eq:associativity} +\end{eqnarray*} +\begin{trulepretest} +\> $\mathbf{D_6}.\text{attributes} = + \text{union}\ (\mathbf{D_2}.\text{attributes}, + \mathbf{D_3}.\text{attributes})\ ;$ +\end{trulepretest} +$\text{is\_associative}\ (\mathbf{D_6}.\text{join\_predicate}, + \mathbf{D_6}.\text{attributes}, + \mathbf{D_5}.\text{join\_predicate})$ +\begin{truleposttest} +\> $\mathbf{D_7} = \mathbf{D_5}\ ;$ \\ +\> $\mathbf{D_7}.\text{join\_predicate} = + \mathbf{D_4}.\text{join\_predicate}\ ;$ \\ +\> $\mathbf{D_6}.\text{tuple\_size} = + \mathbf{D_2}.\text{tuple\_size} + + \mathbf{D_3}.\text{tuple\_size}\ ;$ \\ +\> $\mathbf{D_6}.\text{num\_records} = + \text{cardinality}\ (\mathbf{D_2}, \mathbf{D_3})\ ;$ +\end{truleposttest} +\end{minipage} +\label{fig:associativity} +} +\end{tabular} +} +\caption{T-rule} +\label{fig:trules} +\end{centeredfigure} + +Transformation rules, or T-rules for short, define equivalences among +pairs of expressions; they define mappings from one operator tree to +another. Let $E$ and $E'$ be expressions that involve only abstract +operators. Equation~(\ref{eq:generaltrule}) (shown in +Figure~\ref{fig:generaltrule}) shows the general form of a T-rule. The +actions of a T-rule define the equivalences between the descriptors of +nodes of the original operator tree $E$ with the nodes of the output +tree $E'$; these actions consist of a series of (C or C++) +assignment\footnote{The actions can be non-assignment statements (like +function calls), but in this case, the P2V pre-processor (described in +Section~\ref{sec:ptov}) needs some hints about the properties that +are changed by the statement in order to correctly categorize each +property. For simplicity, in this paper, we assume all actions consist +of assignment statements.} statements. The left-hand sides of these +statements refer to descriptors of expressions on the right-hand side +of the T-rule; the right-hand sides of the statements can refer to any +descriptor in the T-rule. Function (called \emph{helper} functions) +calls can also appear on the right side of the assignment statements. +Thus, descriptors on the \emph{left-hand side} of a T-rule are +\emph{never} changed in the rule's actions. A \emph{test} is needed to +determine if the transformations of the T-rule are in fact applicable. + +Purely as an optimization, it is usually the case that not all +statements in a T-rule's actions need to be executed prior to a +T-rule's test. For this reason, the actions of a T-rule are split into +two groups; those that need to be executed prior to the T-rule's test, +and those that can be executed after a successful test. These groups +of statements comprise, respectively, the \emph{pre-test} and +\emph{post-test} statements of the T-rule.\footnote{We suspect it is +possible to use data-flow analysis to partition the assignment +statements automatically, but for now, we let the rule-writer do the +partitioning.} + +\begin{comment} +We now define the actions and tests of a T-rule more precisely. Let +$O_i$ be an abstract operator of $E'$, and let $\mathbf{O_i}$ be its +descriptor. Similarly, let $I_i$ be an abstract operator of $E$ and +let $\mathbf{I_i}$ be its descriptor. ($I_i$ is an operator that is +input to the rule and $O_i$ is an operator that is output by the +rule). Let $M_i$ denote the $i$th descriptor property. Thus, +$\mathbf{O_i}.M_j$ is the value of the $j$th property of descriptor +$\mathbf{O_i}$. We have found that actions of a T-rule are invariably +assignment statements, since actions compute assignments to descriptor +properties. Rather than admitting all possible computations, we will +present our model in terms of assignment statements.\footnote{ The +actions can be non-assignment statements (like function calls), but in +this case, the P2V pre-processor (described in +Section~\ref{sec:results}) needs some hints about the properties that +are changed by the statement in order to correctly categorize each +property. For simplicity, in this paper, we assume all actions consist +of assignment statements. } The left-hand side of an assignment refers +to an output descriptor ($\mathbf{O_i}$) or a member of an output +descriptor ($\mathbf{O_i}.M_j$). The right-hand side is an expression +or function that only references input descriptors and/or their +members. (We call such functions \emph{helper} functions; they are +defined externally to a rule). Here are a few examples: +\[ +\begin{array}{rlll} +\mathbf{O_i} & = & \mathbf{I_k}\ ; & + \text{$//$ copy descriptor $\mathbf{I_k}$ to $\mathbf{O_i}$} \nonumber \\ +\mathbf{O_i}.M_j & = & \mathbf{I_k}.M_j + 4\ ; & + \text{$//$ expression defining $\mathbf{O_i}.M_j$} \nonumber \\ +\mathbf{O_3}.M_5 & = & \text{helper}\ (\mathbf{I_1}.M_5, \mathbf{I_2}.M_5)\ ; & + \text{$//$ helper function that computes $\mathbf{O_3}.M_5$} \nonumber \\ +& & & + \text{$//$ from inputs $\mathbf{I_1}.M_5$ and $\mathbf{I_2}.M_5$.} \nonumber +\end{array} +\] + +The test for a T-rule's applicability is a boolean expression and +normally involves checks on the values of output descriptors (\eg +$\mathbf{O_3}.M_5 > 6$); occasionally, helper functions may be needed. + +Again, it is important to remember that the pre-test actions are +carried out prior to the test; the post-test actions are performed only +if a T-rule's test evaluates to TRUE, and all post-test actions are +performed immediately, with no intermediate optimization of any +descendant nodes of the root of $E$. + +Note that there are no actions that are carried out \emph{after} the +essential parameters of the root of $E$ are optimized. This is because +a T-rule only logically transforms a conceptual tree into another +conceptual tree. +\end{comment} + +\begin{example} +\label{ex:joinassociativity} +The associativity of JOINs is expressed by T-rule +(\ref{eq:associativity}) in Figure~\ref{fig:associativity}. +\end{example} + +\begin{comment} + + b2=c1 JOIN JOIN a1=b1 + /\ /\ + / \ / \ + a1=b1 JOIN RET RET JOIN b2=c1 + /\ | ====> | /\ + / \ R3 R1 / \ + RET RET RET RET + | | | | + R1 R2 R2 R3 + + a2=c1 JOIN JOIN a1=b1 + /\ /\ + / \ / \ + a1=b1 JOIN RET RET JOIN <empty> + /\ | ==/==> | /\ + / \ R3 R1 / \ + RET RET RET RET + | | | | + R1 R2 R2 R3 + +\end{comment} + +\newsavebox{\lefttreeone} +\newsavebox{\righttreeone} +\newsavebox{\lefttreetwo} +\newsavebox{\righttreetwo} +\newsavebox{\rewritesto} +\newsavebox{\doesnotrewriteto} + +\begin{lrbox}{\lefttreeone} +\begin{minipage}[t]{3.0cm} +\psset{unit=\edgesizes} +\psset{nodesep=3pt} +\nodesizes +\begin{center} +\begin{pspicture}(-0.5,0)(3,3) +\rput(2,3){\rnode{joinr1r2r3}{JOIN}} +\rput(0.5,3){$b_2 = c_1$} +\rput(1,2){\rnode{joinr1r2}{JOIN}} +\rput(-0.5,2){$a_1 = b_1$} +\rput(0,1){\rnode{retr1}{RET}} +\rput(2,1){\rnode{retr2}{RET}} +\rput(3,2){\rnode{retr3}{RET}} +\rput(0,0){\rnode{r1}{$R_1$}} +\rput(2,0){\rnode{r2}{$R_2$}} +\rput(3,1){\rnode{r3}{$R_3$}} +\ncline{-}{joinr1r2}{retr1} +\ncline{-}{joinr1r2}{retr2} +\ncline{-}{joinr1r2r3}{joinr1r2} +\ncline{-}{joinr1r2r3}{retr3} +\ncline{-}{retr1}{r1} +\ncline{-}{retr2}{r2} +\ncline{-}{retr3}{r3} +\end{pspicture} +\end{center} +\end{minipage} +\end{lrbox} + +\begin{lrbox}{\rewritesto} +\begin{minipage}[t]{0.6cm} +\psset{unit=\edgesizes} +\psset{nodesep=3pt} +\nodesizes +\begin{center} +\begin{pspicture}(0,0)(1,3) +\rput(0.5,1.5){$\Longrightarrow$} +\end{pspicture} +\end{center} +\end{minipage} +\end{lrbox} + +\begin{lrbox}{\righttreeone} +\begin{minipage}[t]{3.0cm} +\psset{unit=\edgesizes} +\psset{nodesep=3pt} +\nodesizes +\begin{center} +\begin{pspicture}(0,0)(3,3) +\rput(1,3){\rnode{joinr1r2r3}{JOIN}} +\rput(2.5,3){$a_1 = b_1$} +\rput(2,2){\rnode{joinr2r3}{JOIN}} +\rput(3.5,2){$b_2 = c_1$} +\rput(0,2){\rnode{retr1}{RET}} +\rput(1,1){\rnode{retr2}{RET}} +\rput(3,1){\rnode{retr3}{RET}} +\rput(0,1){\rnode{r1}{$R_1$}} +\rput(1,0){\rnode{r2}{$R_2$}} +\rput(3,0){\rnode{r3}{$R_3$}} +\ncline{-}{joinr1r2r3}{retr1} +\ncline{-}{joinr1r2r3}{joinr2r3} +\ncline{-}{joinr2r3}{retr2} +\ncline{-}{joinr2r3}{retr3} +\ncline{-}{retr1}{r1} +\ncline{-}{retr2}{r2} +\ncline{-}{retr3}{r3} +\end{pspicture} +\end{center} +\end{minipage} +\end{lrbox} + +\begin{lrbox}{\lefttreetwo} +\begin{minipage}[t]{3.0cm} +\psset{unit=\edgesizes} +\psset{nodesep=3pt} +\nodesizes +\begin{center} +\begin{pspicture}(-0.5,0)(3,3) +\rput(2,3){\rnode{joinr1r2r3}{JOIN}} +\rput(0.5,3){$a_2 = c_1$} +\rput(1,2){\rnode{joinr1r2}{JOIN}} +\rput(-0.5,2){$a_1 = b_1$} +\rput(0,1){\rnode{retr1}{RET}} +\rput(2,1){\rnode{retr2}{RET}} +\rput(3,2){\rnode{retr3}{RET}} +\rput(0,0){\rnode{r1}{$R_1$}} +\rput(2,0){\rnode{r2}{$R_2$}} +\rput(3,1){\rnode{r3}{$R_3$}} +\ncline{-}{joinr1r2}{retr1} +\ncline{-}{joinr1r2}{retr2} +\ncline{-}{joinr1r2r3}{joinr1r2} +\ncline{-}{joinr1r2r3}{retr3} +\ncline{-}{retr1}{r1} +\ncline{-}{retr2}{r2} +\ncline{-}{retr3}{r3} +\end{pspicture} +\end{center} +\end{minipage} +\end{lrbox} + +\begin{lrbox}{\doesnotrewriteto} +\begin{minipage}[t]{0.6cm} +\psset{unit=\edgesizes} +\psset{nodesep=3pt} +\nodesizes +\begin{center} +\begin{pspicture}(0,0)(1,3) +\rput(0.5,1.5){$\Longrightarrow$} +\rput(0.5,1.5){$/$} +\end{pspicture} +\end{center} +\end{minipage} +\end{lrbox} + +\begin{lrbox}{\righttreetwo} +\begin{minipage}[t]{3.0cm} +\psset{unit=\edgesizes} +\psset{nodesep=3pt} +\nodesizes +\begin{center} +\begin{pspicture}(0,0)(3,3) +\rput(1,3){\rnode{joinr1r2r3}{JOIN}} +\rput(2,2){\rnode{joinr2r3}{JOIN}} +\rput(0,2){\rnode{retr1}{RET}} +\rput(1,1){\rnode{retr2}{RET}} +\rput(3,1){\rnode{retr3}{RET}} +\rput(0,1){\rnode{r1}{$R_1$}} +\rput(1,0){\rnode{r2}{$R_2$}} +\rput(3,0){\rnode{r3}{$R_3$}} +\ncline{-}{joinr1r2r3}{retr1} +\ncline{-}{joinr1r2r3}{joinr2r3} +\ncline{-}{joinr2r3}{retr2} +\ncline{-}{joinr2r3}{retr3} +\ncline{-}{retr1}{r1} +\ncline{-}{retr2}{r2} +\ncline{-}{retr3}{r3} +\end{pspicture} +\end{center} +\end{minipage} +\end{lrbox} + +\subsection{Implementation rules} +\label{sec:irules} + +Implementation rules, or I-rules for short, define equivalences between +expressions and their implementing algorithms. Let $E$ be an +expression and $A$ be an algorithm that implements $E$. The general +form of an I-rule is given by Equation~(\ref{eq:generalirule}) (shown +in Figure~\ref{fig:generalirule}). + +\begin{centeredfigure} +\def\subfigtopskip{0pt} +\myshadowbox{ +\begin{tabular}{c} +\subfigure[General form of an I-rule] +{ +\setlength{\topsep}{0pt} +\scriptsize +\begin{minipage}[b]{0.86\linewidth} +\begin{irule} +E(x_1, \ldots, x_n):\mathbf{D_1} \Longrightarrow + A(x_1, \ldots, x_n):\mathbf{D_2} \label{eq:generalirule} +\end{irule} +test +\begin{irulepreopt} +\> pre-opt statements +\end{irulepreopt} +\begin{irulepostopt} +\> post-opt statements +\end{irulepostopt} +\end{minipage} +\label{fig:generalirule} +} \\ \hline +%%% +\subfigure[Merge-sort sort algorithm] +{ +\setlength{\topsep}{0pt} +\scriptsize +\begin{minipage}[b]{0.86\linewidth} +\vspace*{4pt} +\begin{irule} +\text{SORT}(S_1):\mathbf{D_2} \Longrightarrow + \text{Merge\_sort}(S_1):\mathbf{D_3} \label{eq:msort} +\end{irule} +$(\mathbf{D_2}.\text{tuple\_order}\ !\negthinspace= \text{DONT\_CARE})$ +\begin{irulepreopt} +\> $\mathbf{D_3} = \mathbf{D_2}\ ;$ +\end{irulepreopt} +\begin{irulepostopt} +\> $\mathbf{D_3}.\text{cost} = \mathbf{D_1}.\text{cost}$ \\ +\> \hspace{1.2cm} $+ (\mathbf{D_3}.\text{num\_records}) * + \log(\mathbf{D_3}.\text{num\_records})\ ;$ +\end{irulepostopt} +\end{minipage} +\label{fig:msort} +} +\end{tabular} +} +\caption{I-rule} +\label{fig:irules} +\end{centeredfigure} + +The actions associated with an I-rule are defined in three parts. +The first part, or \emph{test}, is a boolean expression whose +value determines whether or not the rule can be applied. + +The second part, or \emph{pre-opt statements}, is a set of descriptor +assignment statements that are executed only if the test is true and +\emph{before} any of the inputs $x_i$ of $E$ are optimized. Additional +parameters of nodes are usually assigned in the pre-opt section. This +is necessary before any of the nodes on the right side can be +optimized. + +The third part, or \emph{post-opt statements}, is a set of descriptor +assignment statements that are executed \emph{after} all $x_i$ are +optimized. Normally, the post-opt statements compute cost properties +that can only be determined once the inputs to the algorithm are +completely optimized and their costs known. This \emph{does not}, +however, imply a bottom-up optimization strategy. It simply means that +although I-rules are applied to parents before their children are +optimized, the \emph{cost} (and other properties in the post-opt +section) of the parent cannot be computed until the children have been +optimized. + +\begin{example} +\label{ex:mergesort} +Equation~(\ref{eq:msort}) (in Figure~\ref{fig:msort}) shows the I-rule +that implements the SORT operator by Merge\_sort. +\end{example} + +\subsection{Null algorithm} +\label{sec:null} +Recall that, in Section~\ref{sec:intro}, we mentioned that Prairie +allows users to treat all operators and algorithms as first-class +objects, \ie all operators and algorithms are explicit, in contrast to +enforcers in Volcano or glue in Starburst. This requires that Prairie +provide a mechanism where users can also ``delete'' one or more of the +explicit operators from expressions. This is done by having a special +class of I-rules that have the form given by +Equation~(\ref{eq:generalnullalg}) in Figure~\ref{fig:generalnullalg}. +The left side of the rule is a single abstract operator $O$ with one +stream input $S_1$. The right side of the rule is an algorithm called +``Null'' with the same stream input but with a different descriptor. +As the name suggests, the Null algorithm is supposed to pass its input +unchanged to algorithms above it in an operator tree. This is +accomplished in the I-rule as follows. + +The test for this I-rule is always TRUE, \ie any node in an operator +tree with $O$ as its operator can be implemented by the Null +algorithm. The actions associated with this rule have a specific +pattern. The pre-opt section consists of three +statements. The first statement copies the descriptor of the operator +$O$ to the algorithm Null. The second statement sets the descriptor of +the stream $S_1$ on the right side to the descriptor of the stream +$S_1$ on the left side. Why is it necessary to do this? The key lies +in the third statement. This statement copies the property +``property'' of the operator $O$ node on the left side to the +``property'' of the input stream $S_1$ on the right side. Since +left-hand side descriptors cannot be changed in an I-rule, a new +descriptor $\mathbf{D_3}$ is necessary for $S_1$ to convey the property +propagation information. + +The post-opt section in the I-rule has only a cost-assignment +statement; this simply sets the cost of the Null node to the cost of +its optimized input stream. + +The Null algorithm, therefore, serves to effectively transform a single +operator to a no-op. + +\begin{example} +Equation~(\ref{eq:nullsort}) (in Figure~\ref{fig:nullsort}) shows the +I-rule that rewrites the SORT operator to use a Null algorithm. +\end{example} + +\begin{centeredfigure} +\def\subfigtopskip{0pt} +\myshadowbox{ +\begin{tabular}{c} +\subfigure[General form of a ``Null'' I-rule] +{ +\setlength{\topsep}{0pt} +\scriptsize +\begin{minipage}[b]{0.86\linewidth} +\begin{irule} +O(S_1):\mathbf{D_2} \Longrightarrow + \text{Null}(S_1:\mathbf{D_3}):\mathbf{D_4} \label{eq:generalnullalg} +\end{irule} +TRUE +\begin{irulepreopt} +\> $\mathbf{D_4} = \mathbf{D_2}\ ;$ \\ +\> $\mathbf{D_3} = \mathbf{D_1}\ ;$ \\ +\> $\mathbf{D_3}.\text{property} = \mathbf{D_2}.\text{property}\ ;$ +\end{irulepreopt} +\begin{irulepostopt} +\> $\mathbf{D_4}.\text{cost} = \mathbf{D_3}.\text{cost}\ ;$ +\end{irulepostopt} +\end{minipage} +\label{fig:generalnullalg} +} +\\ \hline +%%% +\subfigure[Null sort algorithm] +{ +\setlength{\topsep}{0pt} +\scriptsize +\begin{minipage}[b]{0.86\linewidth} +\vspace*{4pt} +\begin{irule} +\text{SORT}(S_1):\mathbf{D_2} \rulespace \Longrightarrow + \text{Null}(S_1:\mathbf{D_3}):\mathbf{D_4} \label{eq:nullsort} +\end{irule} +TRUE +\begin{irulepreopt} +\> $\mathbf{D_4} = \mathbf{D_2}\ ;$ \\ +\> $\mathbf{D_3} = \mathbf{D_1}\ ;$ \\ +\> $\mathbf{D_3}.\text{tuple\_order} = \mathbf{D_2}.\text{tuple\_order}\ ;$ +\end{irulepreopt} +\begin{irulepostopt} +\> $\mathbf{D_4}.\text{cost} = \mathbf{D_3}.\text{cost}\ ;$ +\end{irulepostopt} +\end{minipage} +\label{fig:nullsort} +} +\end{tabular} +} +\caption{The ``Null'' algorithm concept} +\label{fig:null} +\end{centeredfigure} diff --git a/macros/latex/contrib/utthesis/ICDE-11/p2v.tex b/macros/latex/contrib/utthesis/ICDE-11/p2v.tex new file mode 100644 index 0000000000..d8c344e302 --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/p2v.tex @@ -0,0 +1,139 @@ +\section{The P2V pre-processor} +\label{sec:ptov} + +In Section~\ref{sec:intro}, we enumerated the four primary goals of +Prairie, viz., uniformity in operator and algorithms; uniformity in +properties; uniformity in property-transformations; and efficient +generation of Prairie optimizers. The first three goals are driven by +the need for conceptual simplicity; however, they alone do not +necessarily generate efficient optimizers. The P2V pre-processor +ensures that efficient optimizers can be realized from Prairie +specifications, by translating them to the Volcano framework and then +generating an optimizer by compiling with the Volcano search engine. +This Prairie optimizer-generator paradigm is shown schematically in +Figure~\ref{fig:ptovmodel}. The pre-processor itself is 4500 lines of +\texttt{flex} and \texttt{bison} code. In this section, we briefly +describe the pre-processor steps and explain why the Prairie-to-Volcano +transformation is non-trivial. A more detailed description of the +pre-processor is given in \cite{Das94}. + +\begin{centeredfigure} +\myshadowbox +{ +\scriptsize +\begin{centeredinfullminipage} +\begin{center} +\psset{unit=6mm} +\psset{nodesep=3pt} +%\begin{pspicture}(-1.0,-0.5)(10,9.0) +\begin{pspicture}(-1.0,-0.5)(8,9.0) +\pspolygon[doubleline=true](1,1.5)(7,1.5)(7,7.5)(1,7.5) +\pspolygon[fillcolor=white,fillstyle=solid](2,8)(6,8)(6,9)(2,9) +\rput(4,8.5){\psframebox*{Prairie Rule Set}} +\psline[border=2pt]{->}(4,8)(4,7) +\pspolygon[doubleline=true](2,6)(6,6)(6,7)(2,7) +\rput(4,6.5){P2V Pre-processor} +\psline[border=2pt]{->}(4,6)(4,5) +\pspolygon[fillcolor=gray,fillstyle=solid](2,4)(6,4)(6,5)(2,5) +\rput(4,4.5){\psframebox*{Volcano Rule Set}} +\psline[border=2pt]{->}(4,4)(4,3) +\pspolygon[doubleline=true](2,2)(6,2)(6,3)(2,3) +\rput(4,2.5){\begin{tabular}{c} Volcano \\ Optimizer-Generator \end{tabular}} +\psline[border=2pt]{->}(4,2)(4,1) +\pspolygon[fillcolor=gray,fillstyle=solid](2,0)(6,0)(6,1)(2,1) +\rput(4,0.5){\psframebox*{Query Optimizer}} +\rput[r](1,0.5){Operator Tree} +\psline[border=2pt]{->}(1,0.5)(2,0.5) +\psline[border=2pt]{->}(6,0.5)(7,0.5) +\rput[l](7,0.5){Access Plan} +\end{pspicture} +\end{center} +\end{centeredinfullminipage} +} +\caption{The Prairie optimizer-generator paradigm. Double-boxed modules + represent software generators, shaded boxes represent + generated programs. The outermost double-boxed portion + denotes the Prairie optimizer generator.} +\label{fig:ptovmodel} +\end{centeredfigure} + +The specification of an optimizer in Volcano consists of a set of +transformation rules (called ``trans\_rules'') and implementation rules +(called ``impl\_rules''), a set of properties, and some support +functions. The join associativity trans\_rule +(cf.\ Figure~\ref{fig:associativity}) in Volcano is as follows\footnote{There +are conditions and actions associated with Volcano rules that are not +shown here.}: +\begin{eqnarray*} +\scriptscriptstyle +& & +{\scriptstyle +(\text{JOIN} \ \text{?op\_arg5} + \ ((\text{JOIN} \ \text{?op\_arg4} \ (?1 \ ?2)) \ + ?3))} \\ +& & +\rulespace +{\scriptstyle -\!\!>} +{\scriptstyle +(\text{JOIN} \ \text{?op\_arg7} + \ (?1 \ + (\text{JOIN} \ \text{?op\_arg6} \ (?2 \ ?3))))} +\end{eqnarray*} +The important point to note is the use of \emph{operator arguments} +(denoted by ``op\_arg'' in rules); these arguments contain properties +used in the rule's actions, but unlike Prairie, they do not contain +\emph{all} the properties of an operator tree node. There are other +property classes, like algorithm argument, logical property, system +property, physical property, and cost. Thus, while Prairie uses a +uniform descriptor to encode properties, Volcano partitions the +properties into different classes. The P2V pre-processor partitions a +Prairie descriptor into the different property classes required by +Volcano. This is a non-trivial task, since it requires parsing the +Prairie rules and their actions. + +Impl\_rules in Volcano defer most of the actions associated with the +rules to support functions. Each algorithm has four support functions +associated with it. A Prairie specification, on the other hand, +contains all the actions in the corresponding rule. The P2V +pre-processor parses a Prairie I-rule, and automatically generates all +the Volcano support functions from the rule. This is also a complex +process, since it depends partly on the partitioning of properties +mentioned in the last paragraph, and also because it requires +relocating pieces of code from Prairie rules to Volcano support +functions. + +The third salient feature of a Volcano specification is the presence of +implicit, or hidden, algorithms, called \emph{enforcers}. In Prairie, +all algorithms are explicit. Consider, for example, the Merge\_sort +algorithm in Figure~\ref{fig:msort}. In a Volcano specification, this +algorithm would be classified as an enforcer, since it enforces the +sortedness property. The P2V pre-processor determines the Prairie +algorithms that are functionally Volcano enforcers, and deletes the +corresponding Prairie rules to generate the Volcano specification. +This requires the pre-processor to migrate the (deleted) rule's actions +to Volcano support functions. + +The P2V pre-processor also generates a set of compact Volcano rules by +merging Prairie rules whenever possible. Consider, for example, the +following set of rules in Prairie: +\begin{eqnarray*} +{\scriptstyle \text{JOIN}(S_1, S_2):\mathbf{D_3}} + & \Longrightarrow & +{\scriptstyle \text{JOPR}(\text{SORT}(S_1):\mathbf{D_4}, + \text{SORT}(S_2):\mathbf{D_5}):\mathbf{D_6}} \\ +{\scriptstyle \text{SORT}(S_1):\mathbf{D_2}} + & \Longrightarrow & +{\scriptstyle \text{Null}(S_1:\mathbf{D_3}):\mathbf{D_4}} \\ +{\scriptstyle \text{JOPR}(S_1, S_2):\mathbf{D_3}} + & \Longrightarrow & +{\scriptstyle \text{Nested\_loops}(S_1:\mathbf{D_4}, S_2):\mathbf{D_5}} +\end{eqnarray*} +The first rule is a T-rule, and the next two are I-rules. The P2V +pre-processor combines the above set of Prairie rules into a single +I-rule, +\begin{eqnarray*} +{\scriptstyle \text{JOIN}(S_1, S_2):\mathbf{D_3}} + & \Longrightarrow & +{\scriptstyle \text{Nested\_loops}(S_1:\mathbf{D_4}, S_2):\mathbf{D_5}} +\end{eqnarray*} +and then translates it into a single Volcano impl\_rule. diff --git a/macros/latex/contrib/utthesis/ICDE-11/paper.aux b/macros/latex/contrib/utthesis/ICDE-11/paper.aux new file mode 100644 index 0000000000..9c07f2af48 --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/paper.aux @@ -0,0 +1,137 @@ +\relax +\citation{Grae93} +\citation{Bato88a} +\citation{Grae87b} +\citation{Haas88} +\citation{Ston86b} +\citation{Haas88,Frey87a,Grae87b,Grae90b} +\citation{Haas88} +\citation{Grae90b} +\@writefile{toc}{\protect \contentsline {section}{\protect \numberline {1}Introduction}{1}} +\newlabel{sec:intro}{{1}{1}} +\@writefile{toc}{\protect \contentsline {section}{\protect \numberline {2}Prairie: A language for rule specification}{2}} +\newlabel{sec:framework}{{2}{2}} +\@writefile{toc}{\protect \contentsline {subsection}{\protect \numberline {2.1}Notation and assumptions}{2}} +\newlabel{sec:notation}{{2.1}{2}} +\@writefile{toc}{\protect \contentsline {paragraph}{Stored Files and Streams.}{2}} +\@writefile{toc}{\protect \contentsline {paragraph}{Database Operations.}{2}} +\@writefile{toc}{\protect \contentsline {paragraph}{Operator Trees.}{2}} +\citation{Seli79} +\citation{Dani82} +\citation{Grae90b} +\@writefile{lot}{\protect \contentsline {table}{\protect \numberline {1}{\ignorespaces Operators and algorithms in a centralized query optimizer and their additional parameters}}{3}} +\newlabel{tab:operators}{{1}{3}} +\@writefile{lot}{\protect \contentsline {table}{\protect \numberline {2}{\ignorespaces Properties of nodes in an operator tree}}{3}} +\newlabel{tab:annotations}{{2}{3}} +\newlabel{fig:optreeexample}{{1(a)}{3}} +\newlabel{fig:accplanexample}{{1(b)}{3}} +\@writefile{lof}{\protect \contentsline {figure}{\protect \numberline {1}{\ignorespaces Example of an operator tree and access plan}}{3}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{1(a)}{\ignorespaces An expression and its corresponding operator tree}}{3}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{1(b)}{\ignorespaces Possible access plan for operator tree in (a)}}{3}} +\newlabel{fig:expexample}{{1}{3}} +\@writefile{toc}{\protect \contentsline {paragraph}{Descriptors.}{3}} +\@writefile{toc}{\protect \contentsline {paragraph}{Access Plans.}{3}} +\@writefile{toc}{\protect \contentsline {subsection}{\protect \numberline {2.2}Prairie optimization paradigm}{3}} +\newlabel{sec:topdown}{{2.2}{3}} +\newlabel{eq:generaltrule}{{1}{4}} +\newlabel{fig:generaltrule}{{2(a)}{4}} +\newlabel{eq:associativity}{{2}{4}} +\newlabel{fig:associativity}{{2(b)}{4}} +\@writefile{lof}{\protect \contentsline {figure}{\protect \numberline {2}{\ignorespaces T-rule}}{4}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{2(a)}{\ignorespaces General form of a T-rule}}{4}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{2(b)}{\ignorespaces Join associativity}}{4}} +\newlabel{fig:trules}{{2}{4}} +\@writefile{toc}{\protect \contentsline {subsection}{\protect \numberline {2.3}Transformation rules}{4}} +\newlabel{sec:trules}{{2.3}{4}} +\newlabel{eq:generalirule}{{3}{4}} +\newlabel{fig:generalirule}{{3(a)}{4}} +\newlabel{eq:msort}{{4}{4}} +\newlabel{fig:msort}{{3(b)}{4}} +\@writefile{lof}{\protect \contentsline {figure}{\protect \numberline {3}{\ignorespaces I-rule}}{4}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{3(a)}{\ignorespaces General form of an I-rule}}{4}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{3(b)}{\ignorespaces Merge-sort sort algorithm}}{4}} +\newlabel{fig:irules}{{3}{4}} +\newlabel{ex:joinassociativity}{{4.}{4}} +\@writefile{toc}{\protect \contentsline {subsection}{\protect \numberline {2.4}Implementation rules}{4}} +\newlabel{sec:irules}{{2.4}{4}} +\citation{Das94} +\newlabel{ex:mergesort}{{5.}{5}} +\@writefile{toc}{\protect \contentsline {subsection}{\protect \numberline {2.5}Null algorithm}{5}} +\newlabel{sec:null}{{2.5}{5}} +\@writefile{toc}{\protect \contentsline {section}{\protect \numberline {3}The P2V pre-processor}{5}} +\newlabel{sec:ptov}{{3}{5}} +\newlabel{eq:generalnullalg}{{5}{5}} +\newlabel{fig:generalnullalg}{{4(a)}{5}} +\newlabel{eq:nullsort}{{6}{5}} +\newlabel{fig:nullsort}{{4(b)}{5}} +\@writefile{lof}{\protect \contentsline {figure}{\protect \numberline {4}{\ignorespaces The ``Null'' algorithm concept}}{5}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{4(a)}{\ignorespaces General form of a ``Null'' I-rule}}{5}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{4(b)}{\ignorespaces Null sort algorithm}}{5}} +\newlabel{fig:null}{{4}{5}} +\citation{Das93} +\citation{Blak93} +\@writefile{lof}{\protect \contentsline {figure}{\protect \numberline {5}{\ignorespaces The Prairie optimizer-generator paradigm. Double-boxed modules represent software generators, shaded boxes represent generated programs. The outermost double-boxed portion denotes the Prairie optimizer generator.}}{6}} +\newlabel{fig:ptovmodel}{{5}{6}} +\@writefile{toc}{\protect \contentsline {section}{\protect \numberline {4}Experimental results}{6}} +\newlabel{sec:results}{{4}{6}} +\@writefile{toc}{\protect \contentsline {subsection}{\protect \numberline {4.1}The Texas Instruments Open OODB query optimizer}{6}} +\newlabel{sec:oodb}{{4.1}{6}} +\@writefile{toc}{\protect \contentsline {subsection}{\protect \numberline {4.2}Programmer productivity}{7}} +\newlabel{sec:productivity}{{4.2}{7}} +\@writefile{toc}{\protect \contentsline {subsection}{\protect \numberline {4.3}Performance results using the Open OODB optimizer}{7}} +\newlabel{sec:oodbexp}{{4.3}{7}} +\citation{Seli79} +\citation{Dani82} +\newlabel{fig:Eone}{{6(a)}{8}} +\newlabel{fig:Etwo}{{6(b)}{8}} +\newlabel{fig:Ethree}{{6(c)}{8}} +\newlabel{fig:Efour}{{6(d)}{8}} +\@writefile{lof}{\protect \contentsline {figure}{\protect \numberline {6}{\ignorespaces Expressions used in generating queries for experiments}}{8}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{6(a)}{\ignorespaces E1}}{8}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{6(b)}{\ignorespaces E2}}{8}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{6(c)}{\ignorespaces E3}}{8}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{6(d)}{\ignorespaces E4}}{8}} +\newlabel{fig:exps}{{6}{8}} +\@writefile{lof}{\protect \contentsline {figure}{\protect \numberline {3}{\ignorespaces Queries used in experiments}}{8}} +\newlabel{tab:queries}{{3}{8}} +\@writefile{toc}{\protect \contentsline {section}{\protect \numberline {5}Related research}{8}} +\newlabel{sec:related}{{5}{8}} +\citation{Haas88} +\citation{Frey87a} +\citation{Grae87b} +\citation{Grae90b} +\newlabel{fig:q1}{{7(a)}{9}} +\newlabel{fig:q2}{{7(b)}{9}} +\newlabel{fig:q3}{{7(c)}{9}} +\newlabel{fig:q4}{{7(d)}{9}} +\newlabel{fig:q5}{{7(e)}{9}} +\newlabel{fig:q6}{{7(f)}{9}} +\newlabel{fig:q7}{{7(g)}{9}} +\newlabel{fig:q8}{{7(h)}{9}} +\@writefile{lof}{\protect \contentsline {figure}{\protect \numberline {7}{\ignorespaces Query optimization times for Q1 through Q8}}{9}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{7(a)}{\ignorespaces Query 1}}{9}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{7(b)}{\ignorespaces Query 2}}{9}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{7(c)}{\ignorespaces Query 3}}{9}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{7(d)}{\ignorespaces Query 4}}{9}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{7(e)}{\ignorespaces Query 5}}{9}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{7(f)}{\ignorespaces Query 6}}{9}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{7(g)}{\ignorespaces Query 7}}{9}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{7(h)}{\ignorespaces Query 8}}{9}} +\newlabel{fig:e4}{{7}{9}} +\@writefile{toc}{\protect \contentsline {section}{\protect \numberline {6}Conclusion and future work}{9}} +\newlabel{sec:conclusion}{{6}{9}} +\bibstyle{plain} +\bibdata{references} +\bibcite{Bato88a}{1} +\bibcite{Blak93}{2} +\bibcite{Dani82}{3} +\bibcite{Das93}{4} +\bibcite{Das94}{5} +\bibcite{Frey87a}{6} +\bibcite{Grae90b}{7} +\bibcite{Grae93}{8} +\bibcite{Grae87b}{9} +\bibcite{Haas88}{10} +\bibcite{Seli79}{11} +\bibcite{Ston86b}{12} +\newlabel{sec:acknowledgments}{{6}{10}} diff --git a/macros/latex/contrib/utthesis/ICDE-11/paper.bbl b/macros/latex/contrib/utthesis/ICDE-11/paper.bbl new file mode 100644 index 0000000000..a7e1b3ccdf --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/paper.bbl @@ -0,0 +1,76 @@ +\begin{thebibliography}{10} + +\bibitem{Bato88a} +D.~S. Batory. +\newblock Building blocks of database management systems. +\newblock Technical Report TR--87--23, The University of Texas at Austin, + February 1988. + +\bibitem{Blak93} +Jos\'e~A. Blakeley, William~J. McKenna, and Goetz Graefe. +\newblock Experiences building the {O}pen {OODB} query optimizer. +\newblock In {\em Proceedings 1993 ACM SIGMOD International Conference on + Management of Data}, pages 287--296, Washington, May 1993. + +\bibitem{Dani82} +Dean Daniels, Patricia Selinger, Laura Haas, Bruce Lindsay, C.~Mohan, Adrian + Walker, and Paul Wilms. +\newblock An introduction to distributed query compilation in {R}$^*$. +\newblock In {\em Proceedings 2nd International Conference on Distributed + Databases}, pages 291--309, Berlin, September 1982. + +\bibitem{Das93} +Dinesh Das and Don Batory. +\newblock Prairie: An algebraic framework for rule specification in query + optimizers. +\newblock In {\em Proceedings of the Workshop on Database Query Optimizer + Generators and Rule-Based Optimizers}, pages 139--154, Dallas, September + 1993. + +\bibitem{Das94} +Dinesh Das and Don Batory. +\newblock Prairie: A rule specification framework for query optimizers. +\newblock Technical Report TR 94--16, The University of Texas at Austin, May + 1994. + +\bibitem{Frey87a} +Johann~Christoph Freytag. +\newblock A rule-based view of query optimization. +\newblock In {\em Proceedings 1987 ACM SIGMOD International Conference on + Management of Data}, pages 173--180, San Francisco, May 1987. + +\bibitem{Grae90b} +Goetz Graefe. +\newblock Volcano, an extensible and parallel query evaluation system. +\newblock Technical Report CU--CS--481--90, University of Colorado at Boulder, + July 1990. + +\bibitem{Grae93} +Goetz Graefe. +\newblock Query evaluation techniques for large databases. +\newblock {\em ACM Computing Surveys}, 25(2):73--170, June 1993. + +\bibitem{Grae87b} +Goetz Graefe and David~J. DeWitt. +\newblock The {EXODUS} optimizer generator. +\newblock In {\em Proceedings 1987 ACM SIGMOD International Conference on + Management of Data}, pages 387--394, San Francisco, May 1987. + +\bibitem{Haas88} +L.~M. Haas, J.~C. Freytag, G.~M. Lohman, and H.~Pirahesh. +\newblock Extensible query processing in {S}tarburst. +\newblock Research Report RJ 6610, IBM Almaden Research Center, December 1988. + +\bibitem{Seli79} +P.~G. Selinger, M.~M. Astrahan, D.~D. Chamberlin, R.~A. Lorie, and T.~G. Price. +\newblock Access path selection in a relational database management system. +\newblock In {\em Proceedings 1979 ACM SIGMOD International Conference on + Management of Data}, pages 23--34, Boston, May 1979. + +\bibitem{Ston86b} +Michael Stonebraker and Lawrence~A. Rowe. +\newblock The design of {P}ostgres. +\newblock In {\em Proceedings 1986 ACM SIGMOD International Conference on + Management of Data}, pages 340--355, Washington, May 1986. + +\end{thebibliography} diff --git a/macros/latex/contrib/utthesis/ICDE-11/paper.blg b/macros/latex/contrib/utthesis/ICDE-11/paper.blg new file mode 100644 index 0000000000..e69de29bb2 --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/paper.blg diff --git a/macros/latex/contrib/utthesis/ICDE-11/paper.dvi b/macros/latex/contrib/utthesis/ICDE-11/paper.dvi Binary files differnew file mode 100644 index 0000000000..24b018fcfb --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/paper.dvi diff --git a/macros/latex/contrib/utthesis/ICDE-11/paper.log b/macros/latex/contrib/utthesis/ICDE-11/paper.log new file mode 100644 index 0000000000..baa677fc30 --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/paper.log @@ -0,0 +1,511 @@ +This is TeX, Version 3.141 (C version d) (format=latex 94.8.3) 20 MAR 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\hbox (badness 10000) has occurred while \output is active +[] + [] + +[1 + + +] +Underfull \hbox (badness 2980) in paragraph at lines 60--68 +[][]\OT1/ptm/m/n/10 A frame-work in which users can spec-ify map-ping + [] + +) (model.tex +LaTeX Font Info: Font shape `OT1/ptm/bx/n' in size <12> not available +(Font) Font shape `OT1/ptm/b/n' tried instead on input line 10. +LaTeX Font Info: Font shape `OT1/ptm/bx/n' in size <10> not available +(Font) Font shape `OT1/ptm/b/n' tried instead on input line 14. +LaTeX Font Info: External font `cmex10' loaded for size +(Font) <7> on input line 16. + +Underfull \hbox (badness 1515) in paragraph at lines 34--42 +\OT1/ptm/m/n/10 are de-noted by all cap-i-tal let-ters (e.g., JOIN). + [] + + +Underfull \hbox (badness 2799) in paragraph at lines 34--42 +\OT1/ptm/m/n/10 tial and ad-di-tional. \OT1/ptm/m/it/10 Es-sen-tial pa-ram-e-te +rs \OT1/ptm/m/n/10 are + [] + + +Underfull \hbox (badness 1354) in paragraph at lines 34--42 +\OT1/ptm/m/n/10 the stream or file in-puts to an op-er-a-tor; these + [] + + +Underfull \hbox (badness 2158) in paragraph at lines 34--42 +\OT1/ptm/m/n/10 are the pri-mary in-puts to be pro-cessed by an + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 44--52 +[][]\OT1/ptm/m/it/10 Algorithms \OT1/ptm/m/n/10 are con-crete im-ple-men- + [] + + +Underfull \hbox (badness 4792) in paragraph at lines 44--52 +\OT1/ptm/m/n/10 ta-tions of con-cep-tual op-er-a-tors; they will be + [] + + +Underfull \hbox (badness 2809) in paragraph at lines 44--52 +\OT1/ptm/m/n/10 rep-re-sented in lower case with the first let-ter + [] + + +Underfull \hbox (badness 8000) in paragraph at lines 44--52 +\OT1/ptm/m/n/10 cap-i-tal-ized (e.g., Nested[]loops). Al-go-rithms + [] + + +Underfull \hbox (badness 2970) in paragraph at lines 44--52 +\OT1/ptm/m/n/10 implement.[] Fur-ther-more, there can be, and + [] + +\first=\skip48 +\second=\skip49 +\third=\skip50 +\fourth=\skip51 +\linelength=\skip52 +LaTeX Font Info: Font shape `OT1/ptm/bx/n' in size <7> not available +(Font) Font shape `OT1/ptm/b/n' tried instead on input line 71. + +Overfull \hbox (12.0pt too wide) in paragraph at lines 85--86 +[]|$[]$| + [] + + +Underfull \hbox (badness 4366) in paragraph at lines 200--200 +[]\OT1/ptm/m/n/8 (a) An ex-pres-sion and its + [] + +[2] +Underfull \hbox (badness 3271) in paragraph at lines 301--311 + []\OT1/ptm/m/n/10 There are two types of al-ge-braic trans-for-ma-tions (or + [] + +[3] +\lefttreeone=\box33 +\righttreeone=\box34 +\lefttreetwo=\box35 +\righttreetwo=\box36 +\rewritesto=\box37 +\doesnotrewriteto=\box38 + [4] +Underfull \hbox (badness 6978) in paragraph at lines 766--769 + []\OT1/ptm/m/n/10 The post-opt sec-tion in the I-rule has only a cost- + [] + + +Underfull \hbox (badness 4699) in paragraph at lines 766--769 + \OT1/ptm/m/n/10 assignment state-ment; this sim-ply sets the cost of the + [] + +) (p2v.tex +Underfull \hbox (badness 1902) in paragraph at lines 4--19 + \OT1/ptm/m/n/10 In Sec-tion 1[], we enu-mer-ated the four pri-mary goals of + [] + + +Underfull \hbox (badness 1577) in paragraph at lines 4--19 + \OT1/ptm/m/n/10 and ef-fi-cient gen-er-a-tion of Prairie op-ti-miz-ers. The fi +rst + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 56--56 +[]\OT1/ptm/m/n/10 Figure 5: The Prairie optimizer-generator paradigm. + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 56--56 +\OT1/ptm/m/n/10 Double-boxed mod-ules rep-re-sent soft-ware gen-er-a-tors, + [] + + +Underfull \hbox (badness 1194) in paragraph at lines 56--56 +\OT1/ptm/m/n/10 shaded boxes rep-re-sent gen-er-ated pro-grams. The out-er- + [] + + +Underfull \hbox (badness 1087) in paragraph at lines 56--56 +\OT1/ptm/m/n/10 most double-boxed por-tion de-notes the Prairie op-ti-mizer + [] + +[5] +Underfull \hbox (badness 1460) in paragraph at lines 105--115 + []\OT1/ptm/m/n/10 The third salient fea-ture of a Vol-cano spec-i-fi-ca-tion i +s + [] + + +Underfull \hbox (badness 2460) in paragraph at lines 105--115 + \OT1/ptm/m/n/10 This re-quires the pre-processor to mi-grate the (deleted) + [] + +) (results.tex +Underfull \hbox (badness 4505) in paragraph at lines 24--26 +[][]\OT1/ptm/m/n/10 How is pro-gram-mer pro-duc-tiv-ity en-hanced by the + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 36--36 + []\OT1/ptm/b/n/12 The Texas In-stru-ments Open OODB + [] + + +Underfull \hbox (badness 5105) in paragraph at lines 39--49 + \OT1/ptm/m/n/10 The Texas In-stru-ments Open Object-Oriented Database + [] + + +Underfull \hbox (badness 7576) in paragraph at lines 39--49 + \OT1/ptm/m/n/10 database sys-tem which pro-vides users an ar-chi-tec-tural + [] + + +Underfull \hbox (badness 1448) in paragraph at lines 39--49 + \OT1/ptm/m/n/10 us-ing Vol-cano. It is writ-ten as a set of trans[]rules and + [] + + +Underfull \hbox (badness 3417) in paragraph at lines 39--49 + \OT1/ptm/m/n/10 impl[]rules that de-fine the al-ge-bra of an object-oriented + [] + + +Underfull \hbox (badness 1122) in paragraph at lines 39--49 + \OT1/ptm/m/n/10 database sys-tem. Cur-rently, there are 17 trans-for-ma-tion + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 39--49 + \OT1/ptm/m/n/10 rules and 9 im-ple-men-ta-tion rules to-gether with about + [] + +[6] +Underfull \hbox (badness 10000) in paragraph at lines 86--86 + []\OT1/ptm/b/n/12 Performance re-sults us-ing the Open + [] + +\Eone=\box39 +\Etwo=\box40 +\Ethree=\box41 +\Efour=\box42 +\c@savectr=\count115 +\Lone=\skip53 +\Ltwo=\skip54 +\Lthree=\skip55 +\Lfour=\skip56 +\Lnum=\skip57 + +Underfull \hbox (badness 10000) in paragraph at lines 351--356 + []\OT1/ptm/m/n/10 Table 3[] also shows the num-ber of trans[]rules and + [] + + +Underfull \hbox (badness 1609) in paragraph at lines 351--356 + \OT1/ptm/m/n/10 impl[]rules that are matched by each ex-pres-sion. These + [] + +[7] +File: runtime_Q1.ps Graphic file (type eps) + <runtime_Q1.ps> +File: runtime_Q2.ps Graphic file (type eps) + <runtime_Q2.ps> +File: runtime_Q3.ps Graphic file (type eps) + <runtime_Q3.ps> +File: runtime_Q4.ps Graphic file (type eps) + <runtime_Q4.ps> +File: runtime_Q5.ps Graphic file (type eps) + +<runtime_Q5.ps> +File: runtime_Q6.ps Graphic file (type eps) + <runtime_Q6.ps> +File: runtime_Q7.ps Graphic file (type eps) + <runtime_Q7.ps> +File: runtime_Q8.ps Graphic file (type eps) + <runtime_Q8.ps>) (related.tex +[8]) (conclusion.tex [9]) (paper.bbl +Underfull \hbox (badness 1292) in paragraph at lines 10--14 +[][]\OT1/ptm/m/n/10 Jos[]e A. Blake-ley, William J. 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Source file was pstricks.doc +% Version 0.93a, 93/03/12. +% For use with Rokicki's dvips. +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/Atan { /atan load stopped { pop pop 0 } if } def +/Div { dup 0 eq { pop } { div } ifelse } def +/NET { neg exch neg exch T } def +/Pyth { dup mul exch dup mul add sqrt } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } +def +/PathLength { flattenpath /z 0 def { /y1 ED /x1 ED /y2 y1 def /x2 x1 def +} { /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } +pathforall z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +/y ED x mul /x ED x 0 eq y 0 eq and { /x 1 def /y 1 def } if [ y x ] 1 a +sub y mul setdash stroke } def +/DotLine { /b PathLength def /a ED /z ED /y CLW def /z y z add def a 0 gt +{ /b b a div def } { a 0 eq { /b b y sub def } { a -3 eq { /b b y add +def } if } ifelse } ifelse [ 0 b b z Div round Div dup 0 le { pop 1 } if +] a 0 gt { 0 } { y 2 div a -2 gt { neg } if } ifelse setdash 1 +setlinecap stroke } def +/LineFill { abs CLW add /a ED gsave clip pathbbox a Div ceiling /y2 ED +/x2 ED a Div floor /y1 ED /x1 ED /n y2 y1 sub 1 add cvi def /y1 a y1 mul +def newpath 2 setlinecap n { currentstrokeadjust == x1 y1 moveto x2 y1 L +stroke /y1 y1 a add def } repeat grestore } def +/LineFill { abs CLW add /a ED gsave clip pathbbox a Div ceiling /y2 ED +/x2 ED a Div floor /y1 ED /x1 ED /n y2 y1 sub 1 add cvi def /y1 a y1 mul +def newpath 2 setlinecap systemdict /currentstrokeadjust known { +currentstrokeadjust } { false } ifelse { /t { } def } { /t { transform +0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform } +bind def } ifelse n { x1 y1 t moveto x2 y1 t L stroke /y1 y1 a add def } +repeat grestore } def +/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg +exch 3 index sub exch Atan rotate newpath } def +/EndArrow { @mtrx setmatrix CP grestore end } def +/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 +scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill +grestore } def +/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0 +CLW moveto } def +/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2 +div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0 +CLW moveto } def +/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW +2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0 +curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto } +def +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { +/closepath load } pathforall ] cvx newpath 3 1 roll T exec } def +/SD { 0 360 arc fill } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch +cvi def } def +/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if +f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub +def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } +ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq +and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } +repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 +ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 +moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto +Lineto pop pop closepath } ifelse } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def +n { NC } repeat EOC } ifelse } def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS +CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { /a 4 string def /b ED /d ED /n ED cvi dup 1 lt { pop 1 } if /c ED +c div dup 0 eq { pop 1 } if /cy ED c div dup 0 eq { pop 1 } if /cx ED cy +div cvi /y ED cx div cvi /x ED cy div cvi /y2 ED cx div cvi /x2 ED cy +div cvi /y1 ED cx div cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse +def /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 +div add def /Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 +div add def } if gsave n 0 gt { 1 setlinecap [ 0 cy n div ] 0 setdash } +{ 2 setlinecap } ifelse /c x1 def /i 500 w mul x1 add def /e y cy mul +def /f y1 cy mul def /g y2 cy mul def x1 cx mul 0 T { newpath 0 e moveto +b 0 gt { gsave d c a cvs dup stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 +add neg} ifelse h 0 gt {b neg} {z1} ifelse rmoveto show grestore } if 0 +f moveto 0 g L stroke cx w mul 0 T c x2 eq c i eq or {exit} if /c c w +add def } loop grestore gsave n 0 gt { 1 setlinecap [ 0 cx n div ] 0 +setdash } { 2 setlinecap } ifelse /c y1 def /i 500 h mul y1 add def /e x +cx mul def /f x1 cx mul def /g x2 cx mul def 0 y1 cy mul T { newpath e 0 +moveto b 0 gt { gsave d c a cvs dup stringwidth pop /z2 ED w 0 gt {z1 z2 +add neg} {z1} ifelse h 0 gt {z1} {b neg} ifelse rmoveto show grestore } +if f 0 moveto g 0 L stroke 0 cy h mul T c y2 eq c i eq or {exit} if /c c +h add def } loop grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /lmtrx [ tx@Dict /lmtrx known { lmtrx aload pop } if CM ] def +CP 4 2 roll T moveto } def +/PutEnd { CP /lmtrx [ lmtrx aload pop setmatrix ] def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { CP OLUnit T +moveto /IfVisible true def } if } { IfVisible { CP OLUnit NET moveto +/IfVisible false def } if } ifelse } def +/InitOL { /OLUnit [ gsave CM STV 2890.79999 dup moveto setmatrix CP +grestore ] cvx def /BOL { BeginOL } def /IfVisible true def } def +end +%%EndProcSet +%%BeginProcSet: /u/ddas/tex/pstricks/ps/pst-node.pro +% PostScript prologue for pst-node.tex. +% Created 1993/3/12. Source file was pst-node.doc +% Version 0.93a, 93/03/12. +% For use with Rokicki's dvips. +/tx@NodeDict 200 dict def tx@NodeDict begin +/NewNode { gsave /next ED dict dup 3 -1 roll ED begin tx@Dict begin STV +CP T exec end /NodeMtrx CM def next end grestore } def +/InitPnode { /Y ED /X ED /NodePos { Nodesep Cos mul Nodesep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { Nodesep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r Nodesep add def } { /dx l Nodesep sub def +} ifelse Sin 0 gt { /dy u Nodesep add def } { /dy d Nodesep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /r ED r mul neg /l ED /r r l add def /X l neg def { neg /d +ED /u ED /Y 0 def } { neg /Y ED Y sub /u ED u mul neg /d ED /u u d add +def /Y Y d sub def } ifelse /NodePos { GetRnodePos } def } def +/InitRNode { /Y ED /X ED /r ED /X r 2 div X add def /r r X sub def /l X +neg def Y add neg /d ED Y sub /u ED /NodePos { GetRnodePos } def } def +/GetOnodePos { /ww w Nodesep add def /hh h Nodesep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/GetAngle { nodeA GetCenter nodeB GetCenter 3 -1 roll sub 3 1 roll sub +neg Atan } def +/GetEdge { begin /Nodesep ED dup 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED NodePos Y add exch X add exch +NodeMtrx transform CM itransform end 4 2 roll 1 index 0 eq { pop pop } { +2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse } def +/GetPos { OffsetA AngleA NodesepA nodeA GetEdge /y1 ED /x1 ED OffsetB +AngleB NodesepB nodeB GetEdge /y2 ED /x2 ED } def +/InitNC { /nodeB ED /nodeA ED /NodesepB ED /NodesepA ED /OffsetB ED +/OffsetA ED tx@NodeDict nodeA known tx@NodeDict nodeB known and dup { +/nodeA nodeA load def /nodeB nodeB load def } if } def +/LineMP { 4 copy 1 t sub mul exch t mul add 3 1 roll 1 t sub mul exch t +mul add exch 6 2 roll sub 3 1 roll sub Atan } def +/NCCoor { GetAngle /AngleA ED /AngleB AngleA 180 add def GetPos /LPutVar +[ x2 x1 y2 y1 ] cvx def /LPutPos { LPutVar LineMP } def x1 y1 x2 y2 } +def +/NCLine { NCCoor tx@Dict begin ArrowB 4 2 roll ArrowA lineto end } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan } def +/GetArms { /x1a armA AngleA cos mul x1 add def /y1a armA AngleA sin mul +y1 add def /x2a armB AngleB cos mul x2 add def /y2a armB AngleB sin mul +y2 add def } def +/NCCurve { GetPos x1 x2 sub y1 y2 sub Pyth 2 div dup 3 -1 roll mul /armA +ED mul /armB ED GetArms x1a y1a x1 y1 tx@Dict begin ArrowA end x2a y2a +x2 y2 tx@Dict begin ArrowB end curveto /LPutVar [ x1 y1 x1a y1a x2a y2a +x2 y2 ] cvx def /LPutPos { t LPutVar BezierMidpoint } def } def +/AnglesMP { LPutVar t 3 gt { /t t 3 sub def } { t 2 gt { /t t 2 sub def +10 -2 roll } { t 1 gt { /t t 1 sub def 10 -4 roll } { 10 4 roll } ifelse +} ifelse } ifelse 6 { pop } repeat 3 -1 roll exch LineMP } def +/NCAngles { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform pop x2a y2a mtrx transform exch pop mtrx itransform /y0 ED /x0 +ED mark armB 0 ne { x2 y2 } if x2a y2a x0 y0 x1a y1a armA 0 ne { x1 y1 } +if tx@Dict begin false Line end /LPutVar [ x2 y2 x2a y2a x0 y0 x1a y1a +x1 y1 ] cvx def /LPutPos { AnglesMP } def } def +/NCAngle { GetPos /x2a armB AngleB cos mul x2 add def /y2a armB AngleB +sin mul y2 add def /mtrx AngleA matrix rotate def x2a y2a mtrx transform +pop x1 y1 mtrx transform exch pop mtrx itransform /y0 ED /x0 ED mark +armB 0 ne { x2 y2 } if x2a y2a x0 y0 x1 y1 tx@Dict begin false Line end +/LPutVar [ x2 y2 x2 y2 x2a y2a x0 y0 x1 y1 ] cvx def /LPutPos { AnglesMP +} def } def +/NCBar { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform pop x2a y2a mtrx transform pop sub dup 0 mtrx itransform 3 -1 +roll 0 gt { /y2a exch y2a add def /x2a exch x2a add def } { /y1a exch +neg y1a add def /x2a exch neg x2a add def } ifelse mark x2 y2 x2a y2a +x1a y1a x1 y1 tx@Dict begin false Line end /LPutVar [ x2 y2 x2 y2 x2a +y2a x1a y1a x1 y1 ] cvx def /LPutPos { LPutVar AnglesMP } def } def +/NCDiag { GetPos GetArms mark x2 y2 x2a y2a x1a y1a x1 y1 tx@Dict begin +false Line end /LPutVar [ x2 y2 x2 y2 x2a y2a x1a y1a x1 y1 ] cvx def +/LPutPos { AnglesMP } def } def +/NCDiagg { OffsetA AngleA NodesepA nodeA GetEdge /y1 ED /x1 ED /x1a armA +AngleA cos mul x1 add def /y1a armA AngleA sin mul y1 add def nodeB +GetCenter y1a sub exch x1a sub Atan 180 add /AngleB ED OffsetB AngleB +NodesepB nodeB GetEdge /y2 ED /x2 ED mark x2 y2 x1a y1a x1 y1 tx@Dict +begin false Line end /LPutVar [ x2 y2 x2 y2 x2 y2 x1a y1a x1 y1] cvx def +/LPutPos { AnglesMP } def } def +/LoopMP { /t t abs def [ LPutVar ] length 2 div 1 sub dup t lt { /t ED } +{ pop } ifelse mark LPutVar t cvi { /t t 1 sub def pop pop } repeat +counttomark 1 add 4 roll cleartomark 3 -1 roll exch LineMP } def +/NCLoop { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform loopsize add /y1b ED /x1b ED /x2b x2a y2a mtrx transform pop +def x2b y1b mtrx itransform /y2b ED /x2b ED x1b y1b mtrx itransform /y1b +ED /x1b ED mark armB 0 ne { x2 y2 } if x2a y2a x2b y2b x1b y1b x1a y1a +armA 0 ne { x1 y1 } if tx@Dict begin false Line end /LPutVar [ x2 y2 x2a +y2a x2b y2b x1b y1b x1a y1a x1 y1 ] cvx def /LPutPos { LoopMP } def } +def +/NCCircle { nodeA GetCenter 0 0 NodesepA nodeA GetEdge pop 3 1 roll /Y ED +/X ED X sub 2 div dup 2 exp r r mul sub abs sqrt atan 2 mul /a ED r +AngleA 90 add PtoC Y add exch X add exch 2 copy /LPutVar [ 4 2 roll r a +] def /LPutPos { LPutVar aload pop t 360 mul add dup 5 1 roll 90 sub +PtoC 3 -1 roll add 3 1 roll add exch 3 -1 roll } def r AngleA 90 sub a +add AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c +57.2957 r Div def /y ED /x ED } def +/LPutCoor { tx@NodeDict /LPutPos known { gsave LPutPos tx@Dict begin +/langle ED CM 3 1 roll STV CP 3 -1 roll sub neg 3 1 roll sub exch moveto +setmatrix CP end grestore } { 0 0 tx@Dict /langle 0 def end } ifelse } +def +end +%%EndProcSet +%%BeginProcSet: texps.pro +TeXDict begin /rf{findfont dup length 1 add dict begin{1 index /FID ne 2 +index /UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type /integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics /Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont /setfont load]cvx def}def +/ObliqueSlant{dup sin S cos div neg}B /SlantFont{4 index mul add}def +/ExtendFont{3 -1 roll mul exch}def /ReEncodeFont{/Encoding exch def}def +end +%%EndProcSet +%%BeginProcSet: special.pro +TeXDict begin /SDict 200 dict N SDict begin /@SpecialDefaults{/hs 612 N +/vs 792 N /ho 0 N /vo 0 N /hsc 1 N /vsc 1 N /ang 0 N /CLIP 0 N /rwiSeen +false N /rhiSeen false N /letter{}N /note{}N /a4{}N /legal{}N}B +/@scaleunit 100 N /@hscale{@scaleunit div /hsc X}B /@vscale{@scaleunit +div /vsc X}B /@hsize{/hs X /CLIP 1 N}B /@vsize{/vs X /CLIP 1 N}B /@clip{ +/CLIP 2 N}B /@hoffset{/ho X}B /@voffset{/vo X}B /@angle{/ang X}B /@rwi{ +10 div /rwi X /rwiSeen true N}B /@rhi{10 div /rhi X /rhiSeen true N}B +/@llx{/llx X}B /@lly{/lly X}B /@urx{/urx X}B /@ury{/ury X}B /magscale +true def end /@MacSetUp{userdict /md known{userdict /md get type +/dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup +length 20 add dict copy def}if end md begin /letter{}N /note{}N /legal{} +N /od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath +clippath mark{transform{itransform moveto}}{transform{itransform lineto} +}{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{ +itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{ +closepath}}pathforall newpath counttomark array astore /gc xdf pop ct 39 +0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if}N +/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 +scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get +ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip +not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 +TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{noflips{TR +pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 +-1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg +TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg +sub neg 0 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0.0 neg 1.0 1.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 152 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + 152 707 a Fa(C)179 719 y Fn(2)142 +618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 142 618 a Fm(RET)-7 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 42 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoingetcl1getcl2 16 { +.5 3.39499 0.05246 false .5 10.8299 InitRnode } NewNode end end + 42 +524 a Fm(JOIN)-7 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a -7 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 182 +415 a + tx@Dict begin 45. Rot end + 182 415 a 143 418 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 143 418 a Fl(:)10 b(:)g(:)182 +415 y + tx@Dict begin 45. neg Rot end + 182 415 a -7 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + -7 699 a 331 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 331 429 a +Fm(RET)336 520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.32748 0.99998 +false .5 8.23895 InitRnode } NewNode end end + 336 520 a Fa(C)364 528 y Fl(n)-7 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 231 335 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.39499 +0.05246 false .5 10.8299 InitRnode } NewNode end end + 231 335 a Fm(JOIN)-7 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + -7 699 +a -7 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 100 881 a Fz(\(a\))17 b(E1)p 447 +976 4 928 v 476 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + 476 707 a Fa(C)504 719 y Fn(1)467 +618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 467 618 a Fm(RET)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 665 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + +665 707 a Fa(C)693 719 y Fn(2)656 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 656 618 a Fm(RET)506 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 463 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl1 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 463 524 a Fm(MA)-5 b(T)506 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl1 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 699 a 652 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl2 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 652 524 a Fm(MA)g(T)506 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 699 a 556 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoinmatgetcl1matgetcl2 +16 { .5 3.39499 0.05246 false .5 10.8299 InitRnode } NewNode end end + 556 429 a Fm(JOIN)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 +699 a 506 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 699 a 695 321 a + tx@Dict begin 45. Rot end + 695 321 a 656 324 +a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 656 324 a Fl(:)11 b(:)f(:)695 321 y + tx@Dict begin 45. neg Rot end + 695 321 a 506 699 +a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 506 699 a 845 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 845 429 a Fm(RET)850 520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.32748 0.99998 +false .5 8.23895 InitRnode } NewNode end end + 850 +520 a Fa(C)878 528 y Fl(n)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 841 335 +a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcln 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 841 335 a Fm(MA)-5 b(T)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodematgetcln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 745 240 +a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.39499 +0.05246 false .5 10.8299 InitRnode } NewNode end end + 745 240 a Fm(JOIN)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 506 699 a 506 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodematgetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 +699 a 611 881 a Fz(\(b\))17 b(E2)p 961 976 4 928 v 990 +707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + 990 707 a Fa(C)1018 719 y Fn(1)981 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 981 618 +a Fm(RET)1020 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1179 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + 1179 707 a +Fa(C)1207 719 y Fn(2)1170 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 1170 618 a Fm(RET)1020 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1070 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoingetcl1getcl2 16 { +.5 3.39499 0.05246 false .5 10.8299 InitRnode } NewNode end end + 1070 524 a Fm(JOIN)1020 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1020 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1209 415 a + tx@Dict begin 45. Rot end + 1209 415 +a 1170 418 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 1170 418 a Fl(:)11 b(:)f(:)1209 415 y + tx@Dict begin 45. neg Rot end + 1209 +415 a 1020 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1020 699 a 1359 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 1359 429 a Fm(RET)1364 +520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.32748 0.99998 +false .5 8.23895 InitRnode } NewNode end end + 1364 520 a Fa(C)1392 528 y Fl(n)1020 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 +699 a 1259 335 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.39499 +0.05246 false .5 10.8299 InitRnode } NewNode end end + 1259 335 a Fm(JOIN)1020 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1020 699 +a 1020 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1227 240 a + tx@Dict begin tx@NodeDict begin { } /TheNodeselect 16 { .5 3.39499 +0.05246 false .5 18.3349 InitRnode } NewNode end end + 1227 240 a Fm(SELECT)1020 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodeselect +/TheNoderoot InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1020 699 a 1127 881 a Fz(\(c\))17 b(E3)p 1474 976 +4 928 v 1504 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + 1504 707 a Fa(C)1531 719 y Fn(1)1495 +618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 1495 618 a Fm(RET)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1693 707 +a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + 1693 707 a Fa(C)1720 719 y Fn(2)1684 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 1684 618 +a Fm(RET)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1490 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl1 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 1490 524 a +Fm(MA)-5 b(T)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl1 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a 1679 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl2 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 1679 524 +a Fm(MA)g(T)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a 1583 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoinmatgetcl1matgetcl2 +16 { .5 3.39499 0.05246 false .5 10.8299 InitRnode } NewNode end end + 1583 429 +a Fm(JOIN)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a 1534 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a +1723 321 a + tx@Dict begin 45. Rot end + 1723 321 a 1684 324 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 1684 324 a Fl(:)10 b(:)h(:)1723 +321 y + tx@Dict begin 45. neg Rot end + 1723 321 a 1534 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1534 699 a 1873 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 1873 +429 a Fm(RET)1878 520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.32748 0.99998 +false .5 8.23895 InitRnode } NewNode end end + 1878 520 a Fa(C)1905 528 y Fl(n)1534 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1868 335 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcln 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 1868 335 a Fm(MA)-5 b(T)1534 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodematgetcln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1772 240 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.39499 +0.05246 false .5 10.8299 InitRnode } NewNode end end + 1772 240 a Fm(JOIN)1534 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1534 699 a 1534 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y(\256cation)h(framework)e(for)i(query)f +(optimizers.)75 b(T)-6 b(echnical)2224 1150 y(Report)22 +b(TR)h(94\26116,)e(The)h(University)g(of)g(T)-6 b(exas)22 +b(at)h(Austin,)2224 1249 y(May)d(1994.)2085 1415 y([6])41 +b(Johann)15 b(Christoph)h(Freytag.)21 b(A)d(rule-based)d(view)h(of)g +(query)2224 1515 y(optimization.)80 b(In)30 b FF(Pr)m(oceedings)f(1987) +h(ACM)h(SIGMOD)2224 1615 y(International)37 b(Confer)m(ence)j(on)f +(Management)f(of)j(Data)p FG(,)2224 1714 y(pages)19 b(173\261180,)e +(San)k(Francisco,)e(May)h(1987.)2085 1880 y([7])41 b(Goetz)33 +b(Graefe.)94 b(V)-11 b(olcano,)36 b(an)d(extensible)g(and)g(parallel) +2224 1980 y(query)23 b(evaluation)g(system.)53 b(T)-6 +b(echnical)24 b(Report)h(CU\261CS\261)2224 2080 y(481\26190,)14 +b(University)i(of)g(Colorado)f(at)i(Boulder)m(,)e(July)i(1990.)2085 +2246 y([8])41 b(Goetz)24 b(Graefe.)48 b(Query)24 b(evaluation)e +(techniques)h(for)h(lar)o(ge)2224 2345 y(databases.)66 +b FF(ACM)28 b(Computing)f(Surveys)p FG(,)i(25\(2\):73\261170,)2224 +2445 y(June)20 b(1993.)2085 2611 y([9])41 b(Goetz)29 +b(Graefe)h(and)f(David)g(J.)i(DeW)m(itt.)78 b(The)30 +b(EXODUS)2224 2710 y(optimizer)21 b(generator)-5 b(.)42 +b(In)23 b FF(Pr)m(oceedings)e(1987)h(ACM)i(SIG-)2224 +2810 y(MOD)40 b(International)d(Confer)m(ence)i(on)g(Management)f(of) +2224 2910 y(Data)p FG(,)19 b(pages)h(387\261394,)d(San)j(Francisco,)g +(May)g(1987.)2044 3076 y([10])40 b(L.)23 b(M.)g(Haas,)h(J.)g(C.)g +(Freytag,)e(G.)i(M.)f(Lohman,)f(and)g(H.)i(Pi-)2224 3175 +y(rahesh.)31 b(Extensible)20 b(query)f(processing)h(in)h(Starburst.)32 +b(Re-)2224 3275 y(search)20 b(Report)g(RJ)i(6610,)e(IBM)h(Almaden)e +(Research)i(Cen-)2224 3375 y(ter)m(,)e(December)g(1988.)2047 +3541 y([1)m(1])40 b(P)-9 b(.)33 b(G.)g(Selinger)m(,)h(M.)f(M.)g +(Astrahan,)i(D.)e(D.)g(Chamberlin,)2224 3640 y(R.)28 +b(A.)h(Lorie,)g(and)f(T)-6 b(.)28 b(G.)g(Price.)69 b(Access)29 +b(path)e(selection)2224 3740 y(in)d(a)g(relational)f(database)g +(management)f(system.)47 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+\PScommands + +\setlength{\mathindent}{0in} + +\renewcommand{\baselinestretch}{1.0} +\newcommand{\eg}{e.g.,\xspace} +\newcommand{\ie}{i.e.,\xspace} +\newcommand{\etc}{etc.\@\xspace} +\makeatletter +\newcommand{\preprint} + {\pagestyle{empty} + \newcommand{\firstpage} + {\thispagestyle{plain} + \makeatletter + \renewcommand{\ps@plain}{ + \renewcommand{\@oddhead}{\fbox{To appear in \textit{Proceedings + 11th International Conference on + Data Engineering}, + Taipei, March 1995}} + \renewcommand{\@evenhead}{} + \renewcommand{\@evenfoot}{} + \renewcommand{\@oddfoot}{}} + \makeatother}} +\newcommand{\reprint} + {\pagestyle{empty} + \newcommand{\firstpage} + {\thispagestyle{plain} + \makeatletter + \renewcommand{\ps@plain}{ + \renewcommand{\@oddhead}{\fbox{In \textit{Proceedings + 11th International Conference on + Data Engineering}, pages 201--210, + Taipei, March 1995}} + \renewcommand{\@evenhead}{} + \renewcommand{\@evenfoot}{} + \renewcommand{\@oddfoot}{}} + \makeatother}} +\makeatother 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+\newenvironment{fullminipage} + {\begin{minipage}[b]{0.93\linewidth}} + {\end{minipage}} + +\newenvironment{fullminipagerule} + {\setlength{\topsep}{0pt} + \scriptsize + \begin{fullminipage}} + {\end{fullminipage}} +\newenvironment{halfminipagerule} + {\setlength{\topsep}{0pt} + \footnotesize + \begin{halfminipage}} + {\end{halfminipage}} + +% Command to add space to second line of rule definitions. +\newcommand{\rulespace}{\quad} +\newenvironment{ruleactions} + {$\doubleopenbraces$ + \begin{tabbing} + \hspace{2pc} \= \kill} + {\end{tabbing} + $\doubleclosebraces$} + +\newenvironment{trule} + {\begin{equation}} + {\end{equation}} +\newenvironment{trulepretest} + {\begin{ruleactions}} + {\end{ruleactions} \\} +\newenvironment{truleposttest} + {\\ + \begin{ruleactions}} + {\end{ruleactions}} +\newenvironment{fullminipagetrule} + {\begin{fullminipagerule}} + {\end{fullminipagerule}} +\newenvironment{halfminipagetrule} + {\begin{halfminipagerule}} + {\end{halfminipagerule}} + +\newenvironment{irule} + {\begin{equation}} + {\end{equation}} +\newenvironment{irulepreopt} + {\\ + \begin{ruleactions}} + {\end{ruleactions}} +\newenvironment{irulepostopt} + {\\ + \begin{ruleactions}} + {\end{ruleactions}} +\newenvironment{fullminipageirule} + {\begin{fullminipagerule}} + {\end{fullminipagerule}} +\newenvironment{halfminipageirule} + {\begin{halfminipagerule}} + {\end{halfminipagerule}} + +\newenvironment{centeredfigure} + {\begin{figure}[tb] + \begin{center}} + {\end{center} + \end{figure}} +\newenvironment{centeredfigure*} + {\begin{figure*}[tb] + \begin{center}} + {\end{center} + \end{figure*}} + +\newenvironment{centeredtable} + {\begin{table}[tb] + \begin{center}} + {\end{center} + \normalsize + \end{table}} +\newenvironment{centeredtable*} + {\begin{table*}[tb] + \begin{center}} + {\end{center} + \normalsize + \end{table*}} + +\newenvironment{centeredinquarterminipage} + {\begin{quarterminipage} + \begin{center}} + {\end{center} + \end{quarterminipage}} +\newenvironment{centeredinhalfminipage} + {\begin{halfminipage} + \begin{center}} + {\end{center} + \end{halfminipage}} +\newenvironment{centeredinfullminipage} + {\begin{fullminipage} + \begin{center}} + {\end{center} + \end{fullminipage}} + +\title{\textbf{Prairie: A Rule Specification Framework \\ + for Query Optimizers}\thanks{ + This research was supported in part by grants from The University + of Texas Applied Research Laboratories, Schlumberger, and + Digital Equipment Corporation.}\ \thanks{ + An expanded version of this paper is available as Technical + Report TR 94--16 by anonymous ftp from \texttt{ftp.cs.utexas.edu}.}} +\author{Dinesh Das \hspace{1in} Don Batory \\ + Department of Computer Sciences \\ + The University of Texas at Austin \\ + Austin, Texas 78712--1188 \\ + \{ddas,batory\}@cs.utexas.edu} +\date{} + +%\final +%\preprint +\reprint + +\makeatletter +\def\thickhline{\noalign{\ifnum0=`}\fi\hrule \@height 1.5pt \futurelet + \@tempa\@xhline} +\makeatother + +\begin{document} + +\maketitle + +\pagenumbering{arabic} +\input{abstract.tex} +\input{intro.tex} +\input{model.tex} +\input{p2v.tex} +\input{results.tex} +\input{related.tex} +\input{conclusion.tex} + +\bibliographystyle{plain} +\bibliography{references} + +\end{document} diff --git a/macros/latex/contrib/utthesis/ICDE-11/preprint.ps b/macros/latex/contrib/utthesis/ICDE-11/preprint.ps new file mode 100644 index 0000000000..00e36a2b29 --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/preprint.ps @@ -0,0 +1,6724 @@ +%!PS-Adobe-2.0 +%%Creator: dvips 5.55 Copyright 1986, 1994 Radical Eye Software +%%Title: paper.dvi +%%CreationDate: Thu Dec 1 10:58:49 1994 +%%Pages: 10 +%%PageOrder: Ascend +%%BoundingBox: 0 0 612 792 +%%DocumentFonts: Times-Roman Times-Italic Times-Bold Courier +%%EndComments +%DVIPSCommandLine: dvips -D 600 paper -o +%DVIPSParameters: dpi=600, comments removed +%DVIPSSource: TeX output 1994.12.01:1057 +%%BeginProcSet: tex.pro +/TeXDict 250 dict def TeXDict begin 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.5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto } +def +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { +/closepath load } pathforall ] cvx newpath 3 1 roll T exec } def +/SD { 0 360 arc fill } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch +cvi def } def +/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if +f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub +def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } +ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq +and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } +repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 +ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 +moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto +Lineto pop pop closepath } ifelse } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def +n { NC } repeat EOC } ifelse } def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS +CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { /a 4 string def /b ED /d ED /n ED cvi dup 1 lt { pop 1 } if /c ED +c div dup 0 eq { pop 1 } if /cy ED c div dup 0 eq { pop 1 } if /cx ED cy +div cvi /y ED cx div cvi /x ED cy div cvi /y2 ED cx div cvi /x2 ED cy +div cvi /y1 ED cx div cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse +def /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 +div add def /Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 +div add def } if gsave n 0 gt { 1 setlinecap [ 0 cy n div ] 0 setdash } +{ 2 setlinecap } ifelse /c x1 def /i 500 w mul x1 add def /e y cy mul +def /f y1 cy mul def /g y2 cy mul def x1 cx mul 0 T { newpath 0 e moveto +b 0 gt { gsave d c a cvs dup stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 +add neg} ifelse h 0 gt {b neg} {z1} ifelse rmoveto show grestore } if 0 +f moveto 0 g L stroke cx w mul 0 T c x2 eq c i eq or {exit} if /c c w +add def } loop grestore gsave n 0 gt { 1 setlinecap [ 0 cx n div ] 0 +setdash } { 2 setlinecap } ifelse /c y1 def /i 500 h mul y1 add def /e x +cx mul def /f x1 cx mul def /g x2 cx mul def 0 y1 cy mul T { newpath e 0 +moveto b 0 gt { gsave d c a cvs dup stringwidth pop /z2 ED w 0 gt {z1 z2 +add neg} {z1} ifelse h 0 gt {z1} {b neg} ifelse rmoveto show grestore } +if f 0 moveto g 0 L stroke 0 cy h mul T c y2 eq c i eq or {exit} if /c c +h add def } loop grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /lmtrx [ tx@Dict /lmtrx known { lmtrx aload pop } if CM ] def +CP 4 2 roll T moveto } def +/PutEnd { CP /lmtrx [ lmtrx aload pop setmatrix ] def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { CP OLUnit T +moveto /IfVisible true def } if } { IfVisible { CP OLUnit NET moveto +/IfVisible false def } if } ifelse } def +/InitOL { /OLUnit [ gsave CM STV 2890.79999 dup moveto setmatrix CP +grestore ] cvx def /BOL { BeginOL } def /IfVisible true def } def +end +%%EndProcSet +%%BeginProcSet: /u/ddas/tex/pstricks/ps/pst-node.pro +% PostScript prologue for pst-node.tex. +% Created 1993/3/12. Source file was pst-node.doc +% Version 0.93a, 93/03/12. +% For use with Rokicki's dvips. +/tx@NodeDict 200 dict def tx@NodeDict begin +/NewNode { gsave /next ED dict dup 3 -1 roll ED begin tx@Dict begin STV +CP T exec end /NodeMtrx CM def next end grestore } def +/InitPnode { /Y ED /X ED /NodePos { Nodesep Cos mul Nodesep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { Nodesep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r Nodesep add def } { /dx l Nodesep sub def +} ifelse Sin 0 gt { /dy u Nodesep add def } { /dy d Nodesep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /r ED r mul neg /l ED /r r l add def /X l neg def { neg /d +ED /u ED /Y 0 def } { neg /Y ED Y sub /u ED u mul neg /d ED /u u d add +def /Y Y d sub def } ifelse /NodePos { GetRnodePos } def } def +/InitRNode { /Y ED /X ED /r ED /X r 2 div X add def /r r X sub def /l X +neg def Y add neg /d ED Y sub /u ED /NodePos { GetRnodePos } def } def +/GetOnodePos { /ww w Nodesep add def /hh h Nodesep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/GetAngle { nodeA GetCenter nodeB GetCenter 3 -1 roll sub 3 1 roll sub +neg Atan } def +/GetEdge { begin /Nodesep ED dup 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED NodePos Y add exch X add exch +NodeMtrx transform CM itransform end 4 2 roll 1 index 0 eq { pop pop } { +2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse } def +/GetPos { OffsetA AngleA NodesepA nodeA GetEdge /y1 ED /x1 ED OffsetB +AngleB NodesepB nodeB GetEdge /y2 ED /x2 ED } def +/InitNC { /nodeB ED /nodeA ED /NodesepB ED /NodesepA ED /OffsetB ED +/OffsetA ED tx@NodeDict nodeA known tx@NodeDict nodeB known and dup { +/nodeA nodeA load def /nodeB nodeB load def } if } def +/LineMP { 4 copy 1 t sub mul exch t mul add 3 1 roll 1 t sub mul exch t +mul add exch 6 2 roll sub 3 1 roll sub Atan } def +/NCCoor { GetAngle /AngleA ED /AngleB AngleA 180 add def GetPos /LPutVar +[ x2 x1 y2 y1 ] cvx def /LPutPos { LPutVar LineMP } def x1 y1 x2 y2 } +def +/NCLine { NCCoor tx@Dict begin ArrowB 4 2 roll ArrowA lineto end } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan } def +/GetArms { /x1a armA AngleA cos mul x1 add def /y1a armA AngleA sin mul +y1 add def /x2a armB AngleB cos mul x2 add def /y2a armB AngleB sin mul +y2 add def } def +/NCCurve { GetPos x1 x2 sub y1 y2 sub Pyth 2 div dup 3 -1 roll mul /armA +ED mul /armB ED GetArms x1a y1a x1 y1 tx@Dict begin ArrowA end x2a y2a +x2 y2 tx@Dict begin ArrowB end curveto /LPutVar [ x1 y1 x1a y1a x2a y2a +x2 y2 ] cvx def /LPutPos { t LPutVar BezierMidpoint } def } def +/AnglesMP { LPutVar t 3 gt { /t t 3 sub def } { t 2 gt { /t t 2 sub def +10 -2 roll } { t 1 gt { /t t 1 sub def 10 -4 roll } { 10 4 roll } ifelse +} ifelse } ifelse 6 { pop } repeat 3 -1 roll exch LineMP } def +/NCAngles { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform pop x2a y2a mtrx transform exch pop mtrx itransform /y0 ED /x0 +ED mark armB 0 ne { x2 y2 } if x2a y2a x0 y0 x1a y1a armA 0 ne { x1 y1 } +if tx@Dict begin false Line end /LPutVar [ x2 y2 x2a y2a x0 y0 x1a y1a +x1 y1 ] cvx def /LPutPos { AnglesMP } def } def +/NCAngle { GetPos /x2a armB AngleB cos mul x2 add def /y2a armB AngleB +sin mul y2 add def /mtrx AngleA matrix rotate def x2a y2a mtrx transform +pop x1 y1 mtrx transform exch pop mtrx itransform /y0 ED /x0 ED mark +armB 0 ne { x2 y2 } if x2a y2a x0 y0 x1 y1 tx@Dict begin false Line end +/LPutVar [ x2 y2 x2 y2 x2a y2a x0 y0 x1 y1 ] cvx def /LPutPos { AnglesMP +} def } def +/NCBar { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform pop x2a y2a mtrx transform pop sub dup 0 mtrx itransform 3 -1 +roll 0 gt { /y2a exch y2a add def /x2a exch x2a add def } { /y1a exch +neg y1a add def /x2a exch neg x2a add def } ifelse mark x2 y2 x2a y2a +x1a y1a x1 y1 tx@Dict begin false Line end /LPutVar [ x2 y2 x2 y2 x2a +y2a x1a y1a x1 y1 ] cvx def /LPutPos { LPutVar AnglesMP } def } def +/NCDiag { GetPos GetArms mark x2 y2 x2a y2a x1a y1a x1 y1 tx@Dict begin +false Line end /LPutVar [ x2 y2 x2 y2 x2a y2a x1a y1a x1 y1 ] cvx def +/LPutPos { AnglesMP } def } def +/NCDiagg { OffsetA AngleA NodesepA nodeA GetEdge /y1 ED /x1 ED /x1a armA +AngleA cos mul x1 add def /y1a armA AngleA sin mul y1 add def nodeB +GetCenter y1a sub exch x1a sub Atan 180 add /AngleB ED OffsetB AngleB +NodesepB nodeB GetEdge /y2 ED /x2 ED mark x2 y2 x1a y1a x1 y1 tx@Dict +begin false Line end /LPutVar [ x2 y2 x2 y2 x2 y2 x1a y1a x1 y1] cvx def +/LPutPos { AnglesMP } def } def +/LoopMP { /t t abs def [ LPutVar ] length 2 div 1 sub dup t lt { /t ED } +{ pop } ifelse mark LPutVar t cvi { /t t 1 sub def pop pop } repeat +counttomark 1 add 4 roll cleartomark 3 -1 roll exch LineMP } def +/NCLoop { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform loopsize add /y1b ED /x1b ED /x2b x2a y2a mtrx transform pop +def x2b y1b mtrx itransform /y2b ED /x2b ED x1b y1b mtrx itransform /y1b +ED /x1b ED mark armB 0 ne { x2 y2 } if x2a y2a x2b y2b x1b y1b x1a y1a +armA 0 ne { x1 y1 } if tx@Dict begin false Line end /LPutVar [ x2 y2 x2a +y2a x2b y2b x1b y1b x1a y1a x1 y1 ] cvx def /LPutPos { LoopMP } def } +def +/NCCircle { nodeA GetCenter 0 0 NodesepA nodeA GetEdge pop 3 1 roll /Y ED +/X ED X sub 2 div dup 2 exp r r mul sub abs sqrt atan 2 mul /a ED r +AngleA 90 add PtoC Y add exch X add exch 2 copy /LPutVar [ 4 2 roll r a +] def /LPutPos { LPutVar aload pop t 360 mul add dup 5 1 roll 90 sub +PtoC 3 -1 roll add 3 1 roll add exch 3 -1 roll } def r AngleA 90 sub a +add AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c +57.2957 r Div def /y ED /x ED } def +/LPutCoor { tx@NodeDict /LPutPos known { gsave LPutPos tx@Dict begin +/langle ED CM 3 1 roll STV CP 3 -1 roll sub neg 3 1 roll sub exch moveto +setmatrix CP end grestore } { 0 0 tx@Dict /langle 0 def end } ifelse } +def +end +%%EndProcSet +%%BeginProcSet: texps.pro +TeXDict begin /rf{findfont dup length 1 add dict begin{1 index /FID ne 2 +index /UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type /integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics /Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont /setfont load]cvx def}def +/ObliqueSlant{dup sin S cos div neg}B /SlantFont{4 index mul add}def +/ExtendFont{3 -1 roll mul exch}def /ReEncodeFont{/Encoding exch def}def +end +%%EndProcSet +%%BeginProcSet: special.pro +TeXDict begin /SDict 200 dict N SDict begin /@SpecialDefaults{/hs 612 N +/vs 792 N /ho 0 N /vo 0 N /hsc 1 N /vsc 1 N /ang 0 N /CLIP 0 N /rwiSeen +false N /rhiSeen false N /letter{}N /note{}N /a4{}N /legal{}N}B +/@scaleunit 100 N /@hscale{@scaleunit div /hsc X}B /@vscale{@scaleunit +div /vsc X}B /@hsize{/hs X /CLIP 1 N}B /@vsize{/vs X /CLIP 1 N}B /@clip{ +/CLIP 2 N}B /@hoffset{/ho X}B /@voffset{/vo X}B /@angle{/ang X}B /@rwi{ +10 div /rwi X /rwiSeen true N}B /@rhi{10 div /rhi X /rhiSeen true N}B +/@llx{/llx X}B /@lly{/lly X}B /@urx{/urx X}B /@ury{/ury X}B /magscale +true def end /@MacSetUp{userdict /md known{userdict /md get type +/dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup +length 20 add dict copy def}if end md begin /letter{}N /note{}N /legal{} +N /od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath +clippath mark{transform{itransform moveto}}{transform{itransform lineto} +}{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{ +itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{ +closepath}}pathforall newpath counttomark array astore /gc xdf pop ct 39 +0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if}N +/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 +scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get +ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip +not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 +TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{noflips{TR +pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 +-1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg +TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg +sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr +0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 -1 roll add +2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N /cp +{pop pop showpage pm restore}N end}if}if}N /normalscale{Resolution 72 +div VResolution 72 div neg scale magscale{DVImag dup scale}if 0 setgray} +N /psfts{S 65781.76 div N}N /startTexFig{/psf$SavedState save N userdict +maxlength dict begin /magscale false def normalscale currentpoint TR +/psf$ury psfts /psf$urx psfts /psf$lly psfts /psf$llx psfts /psf$y psfts +/psf$x psfts currentpoint /psf$cy X /psf$cx X /psf$sx psf$x psf$urx +psf$llx sub div N /psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy +scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub TR +/showpage{}N /erasepage{}N /copypage{}N /p 3 def @MacSetUp}N /doclip{ +psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 +roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath +moveto}N /endTexFig{end psf$SavedState restore}N /@beginspecial{SDict +begin /SpecialSave save N gsave normalscale currentpoint TR +@SpecialDefaults count /ocount X /dcount countdictstack N}N /@setspecial +{CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto +closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx +sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR +}{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse +CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury +lineto closepath clip}if /showpage{}N /erasepage{}N /copypage{}N newpath +}N /@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{ +end}repeat grestore SpecialSave restore end}N /@defspecial{SDict begin} +N /@fedspecial{end}B /li{lineto}B /rl{rlineto}B /rc{rcurveto}B /np{ +/SaveX currentpoint /SaveY X N 1 setlinecap newpath}N /st{stroke SaveX +SaveY moveto}N /fil{fill SaveX SaveY moveto}N /ellipse{/endangle X +/startangle X /yrad X /xrad X /savematrix matrix currentmatrix N TR xrad +yrad scale 0 0 1 startangle endangle arc savematrix setmatrix}N end +%%EndProcSet +TeXDict begin @defspecial + + TeXDict begin /box{newpath 2 copy moveto 3 copy pop exch lineto 4 +copy pop pop lineto 4 copy exch pop exch pop lineto closepath } bind +def /min{ 2 copy gt { exch } if pop } bind def/max{ 2 copy lt { exch +} if pop } bind def/roundedbox{/radius exch store 3 2 roll 2 copy min +radius sub /miny exch store max radius add /maxy exch store 2 copy +min radius sub /minx exch store max radius add /maxx exch store newpath +minx radius add miny moveto maxx miny maxx maxy radius arcto maxx maxy +minx maxy radius arcto minx maxy minx miny radius arcto minx miny maxx +miny radius arcto 16 {pop} repeat closepath }bind def /rectcartouche{box +gsave .95 setgray fill grestore 1 setlinewidth stroke }bind def /cartouche{roundedbox +gsave .95 setgray fill grestore 1 setlinewidth stroke }bind def end 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/TheNodegetcl1 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + -47 618 a Fm(RET)-7 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 152 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 3.37999 1.5 +false .5 7.23782 InitRnode } NewNode end end + 152 707 a Fa(C)179 719 y Fn(2)142 +618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + 142 618 a Fm(RET)-7 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 42 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoingetcl1getcl2 16 { +.5 3.36499 0.06248 false .5 10.82999 InitRnode } NewNode end end + 42 +524 a Fm(JOIN)-7 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a -7 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 182 +415 a + tx@Dict begin 45. Rot end + 182 415 a 143 418 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 143 418 a Fl(:)10 b(:)g(:)182 +415 y + tx@Dict begin 45. neg Rot end + 182 415 a -7 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + -7 699 a 331 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + 331 429 a +Fm(RET)336 520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.37999 0.99998 +false .5 8.23898 InitRnode } NewNode end end + 336 520 a Fa(C)364 528 y Fl(n)-7 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 231 335 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.36499 +0.06248 false .5 10.82999 InitRnode } NewNode end end + 231 335 a Fm(JOIN)-7 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + -7 699 +a -7 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 100 881 a Fz(\(a\))17 b(E1)p 447 +976 4 928 v 476 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 3.37999 1.5 +false .5 7.23782 InitRnode } NewNode end end + 476 707 a Fa(C)504 719 y Fn(1)467 +618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + 467 618 a Fm(RET)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 665 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 3.37999 1.5 +false .5 7.23782 InitRnode } NewNode end end + +665 707 a Fa(C)693 719 y Fn(2)656 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + 656 618 a Fm(RET)506 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 463 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl1 16 { .5 3.36499 +0.0 false .5 10.55498 InitRnode } NewNode end end + 463 524 a Fm(MA)-5 b(T)506 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl1 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 699 a 652 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl2 16 { .5 3.36499 +0.0 false .5 10.55498 InitRnode } NewNode end end + 652 524 a Fm(MA)g(T)506 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 699 a 556 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoinmatgetcl1matgetcl2 +16 { .5 3.36499 0.06248 false .5 10.82999 InitRnode } NewNode end +end + 556 429 a Fm(JOIN)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 +699 a 506 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 699 a 695 321 a + tx@Dict begin 45. Rot end + 695 321 a 656 324 +a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 656 324 a Fl(:)11 b(:)f(:)695 321 y + tx@Dict begin 45. neg Rot end + 695 321 a 506 699 +a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 506 699 a 845 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + 845 429 a Fm(RET)850 520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.37999 0.99998 +false .5 8.23898 InitRnode } NewNode end end + 850 +520 a Fa(C)878 528 y Fl(n)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 841 335 +a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcln 16 { .5 3.36499 +0.0 false .5 10.55498 InitRnode } NewNode end end + 841 335 a Fm(MA)-5 b(T)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodematgetcln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 745 240 +a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.36499 +0.06248 false .5 10.82999 InitRnode } NewNode end end + 745 240 a Fm(JOIN)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 506 699 a 506 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodematgetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 +699 a 611 881 a Fz(\(b\))17 b(E2)p 961 976 4 928 v 990 +707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 3.37999 1.5 +false .5 7.23782 InitRnode } NewNode end end + 990 707 a Fa(C)1018 719 y Fn(1)981 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + 981 618 +a Fm(RET)1020 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1179 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 3.37999 1.5 +false .5 7.23782 InitRnode } NewNode end end + 1179 707 a +Fa(C)1207 719 y Fn(2)1170 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + 1170 618 a Fm(RET)1020 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1070 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoingetcl1getcl2 16 { +.5 3.36499 0.06248 false .5 10.82999 InitRnode } NewNode end end + 1070 524 a Fm(JOIN)1020 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1020 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1209 415 a + tx@Dict begin 45. Rot end + 1209 415 +a 1170 418 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 1170 418 a Fl(:)11 b(:)f(:)1209 415 y + tx@Dict begin 45. neg Rot end + 1209 +415 a 1020 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1020 699 a 1359 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + 1359 429 a Fm(RET)1364 +520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.37999 0.99998 +false .5 8.23898 InitRnode } NewNode end end + 1364 520 a Fa(C)1392 528 y Fl(n)1020 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 +699 a 1259 335 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.36499 +0.06248 false .5 10.82999 InitRnode } NewNode end end + 1259 335 a Fm(JOIN)1020 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1020 699 +a 1020 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1227 240 a + tx@Dict begin tx@NodeDict begin { } /TheNodeselect 16 { .5 3.36499 +0.06248 false .5 18.33496 InitRnode } NewNode end end + 1227 240 a Fm(SELECT)1020 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodeselect +/TheNoderoot InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1020 699 a 1127 881 a Fz(\(c\))17 b(E3)p 1474 976 +4 928 v 1504 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 3.37999 1.5 +false .5 7.23782 InitRnode } NewNode end end + 1504 707 a Fa(C)1531 719 y Fn(1)1495 +618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + 1495 618 a Fm(RET)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1693 707 +a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 3.37999 1.5 +false .5 7.23782 InitRnode } NewNode end end + 1693 707 a Fa(C)1720 719 y Fn(2)1684 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + 1684 618 +a Fm(RET)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1490 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl1 16 { .5 3.36499 +0.0 false .5 10.55498 InitRnode } NewNode end end + 1490 524 a +Fm(MA)-5 b(T)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl1 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a 1679 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl2 16 { .5 3.36499 +0.0 false .5 10.55498 InitRnode } NewNode end end + 1679 524 +a Fm(MA)g(T)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a 1583 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoinmatgetcl1matgetcl2 +16 { .5 3.36499 0.06248 false .5 10.82999 InitRnode } NewNode end +end + 1583 429 +a Fm(JOIN)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a 1534 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a +1723 321 a + tx@Dict begin 45. Rot end + 1723 321 a 1684 324 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 1684 324 a Fl(:)10 b(:)h(:)1723 +321 y + tx@Dict begin 45. neg Rot end + 1723 321 a 1534 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1534 699 a 1873 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + 1873 +429 a Fm(RET)1878 520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.37999 0.99998 +false .5 8.23898 InitRnode } NewNode end end + 1878 520 a Fa(C)1905 528 y Fl(n)1534 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1868 335 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcln 16 { .5 3.36499 +0.0 false .5 10.55498 InitRnode } NewNode end end + 1868 335 a Fm(MA)-5 b(T)1534 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodematgetcln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1772 240 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.36499 +0.06248 false .5 10.82999 InitRnode } NewNode end end + 1772 240 a Fm(JOIN)1534 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1534 699 a 1534 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b/macros/latex/contrib/utthesis/ICDE-11/related.tex @@ -0,0 +1,59 @@ +\section{Related research} +\label{sec:related} + +The System R optimizer \cite{Seli79} was the most important development +in query optimization research. It was a cost-based centralized +relational query optimizer and introduced a variety of key concepts +like ``interesting'' expressions, cardinality estimation using +selectivity factors and dynamic programming with pruning of search +space. These concepts continue to be important in query optimizer +research. + +The query optimizer in R$^*$ \cite{Dani82} works in essentially +the same way as that of System R, except that R$^*$ is a distributed +database system which introduces some subtle complications in its query +optimizer. + +The Starburst query optimizer \cite{Haas88} uses rules for all +decisions that need to be taken by the query optimizer. The rules are +functional in nature and transform a given operator tree into another. +The rules are commonly those that reflect relational calculus facts. +In Starburst, the query rewriting phase is different from the +optimization phase. The rewriting phase transforms the query itself +into equivalent operator trees based on relational calculus rules. The +plan optimization phase selects algorithms for each operator in the +operator tree that is obtained after rewriting. The disadvantage of +separating the query rewrite and the optimization phases is that +pruning of the search space is not possible during query rewrite, since +the rewrite phase is non-cost-based. + +Freytag \cite{Frey87a} describes a rule-based query optimizer similar +to Starburst. The rules are based on LISP-like representations of +access plans. The rules themselves are recursively defined on smaller +expressions (operator trees). Although several expressions can contain +a common sub-expression, Freytag doesn't consider the possibility of +sharing. Expressions are evaluated each time they are encountered. +This is obviously inefficient. In addition, as in Starburst, he +doesn't consider the cost transformations inherent in any query +optimizer; rules are syntactic transformation rules. + +EXODUS \cite{Grae87b} provides an optimizer generator which accepts a +rule-based specification of the data model as input. The optimizer +generator compiles these rules, together with pre-defined rules, to +generate an optimizer for the particular data model and set of +operators. Unlike Freytag, the optimizer generator for EXODUS allows +for C code along with definitions of new rules. This allows the +database implementor the freedom to associate any action with a +particular rule. Operator trees in EXODUS are constructed bottom-up +from previously constructed trees. + +The Volcano optimizer generator project \cite{Grae90b} evolved from the +EXODUS project. It is different from all the above optimizers in one +significant way: it is a top-down optimizer compared with the bottom-up +strategy of the others. Operator trees are optimized starting from the +root while sub-trees are not yet optimized. This leads to a +constraint-driven generation of the search space. While this method +results in a tight control of the search space, it is unconventional +and requires careful attention on the part of the optimizer implementor +to ensure that legal operator trees are not accidently left out of +the search space. 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CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def +n { NC } repeat EOC } ifelse } def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS +CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { /a 4 string def /b ED /d ED /n ED cvi dup 1 lt { pop 1 } if /c ED +c div dup 0 eq { pop 1 } if /cy ED c div dup 0 eq { pop 1 } if /cx ED cy +div cvi /y ED cx div cvi /x ED cy div cvi /y2 ED cx div cvi /x2 ED cy +div cvi /y1 ED cx div cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse +def /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 +div add def /Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 +div add def } if gsave n 0 gt { 1 setlinecap [ 0 cy n div ] 0 setdash } +{ 2 setlinecap } ifelse /c x1 def /i 500 w mul x1 add def /e y cy mul +def /f y1 cy mul def /g y2 cy mul def x1 cx mul 0 T { newpath 0 e moveto +b 0 gt { gsave d c a cvs dup stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 +add neg} ifelse h 0 gt {b neg} {z1} ifelse rmoveto show grestore } if 0 +f moveto 0 g L stroke cx w mul 0 T c x2 eq c i eq or {exit} if /c c w +add def } loop grestore gsave n 0 gt { 1 setlinecap [ 0 cx n div ] 0 +setdash } { 2 setlinecap } ifelse /c y1 def /i 500 h mul y1 add def /e x +cx mul def /f x1 cx mul def /g x2 cx mul def 0 y1 cy mul T { newpath e 0 +moveto b 0 gt { gsave d c a cvs dup stringwidth pop /z2 ED w 0 gt {z1 z2 +add neg} {z1} ifelse h 0 gt {z1} {b neg} ifelse rmoveto show grestore } +if f 0 moveto g 0 L stroke 0 cy h mul T c y2 eq c i eq or {exit} if /c c +h add def } loop grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /lmtrx [ tx@Dict /lmtrx known { lmtrx aload pop } if CM ] def +CP 4 2 roll T moveto } def +/PutEnd { CP /lmtrx [ lmtrx aload pop setmatrix ] def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { CP OLUnit T +moveto /IfVisible true def } if } { IfVisible { CP OLUnit NET moveto +/IfVisible false def } if } ifelse } def +/InitOL { /OLUnit [ gsave CM STV 2890.79999 dup moveto setmatrix CP +grestore ] cvx def /BOL { BeginOL } def /IfVisible true def } def +end +%%EndProcSet +%%BeginProcSet: /u/ddas/tex/pstricks/ps/pst-node.pro +% PostScript prologue for pst-node.tex. +% Created 1993/3/12. Source file was pst-node.doc +% Version 0.93a, 93/03/12. +% For use with Rokicki's dvips. +/tx@NodeDict 200 dict def tx@NodeDict begin +/NewNode { gsave /next ED dict dup 3 -1 roll ED begin tx@Dict begin STV +CP T exec end /NodeMtrx CM def next end grestore } def +/InitPnode { /Y ED /X ED /NodePos { Nodesep Cos mul Nodesep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { Nodesep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r Nodesep add def } { /dx l Nodesep sub def +} ifelse Sin 0 gt { /dy u Nodesep add def } { /dy d Nodesep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /r ED r mul neg /l ED /r r l add def /X l neg def { neg /d +ED /u ED /Y 0 def } { neg /Y ED Y sub /u ED u mul neg /d ED /u u d add +def /Y Y d sub def } ifelse /NodePos { GetRnodePos } def } def +/InitRNode { /Y ED /X ED /r ED /X r 2 div X add def /r r X sub def /l X +neg def Y add neg /d ED Y sub /u ED /NodePos { GetRnodePos } def } def +/GetOnodePos { /ww w Nodesep add def /hh h Nodesep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/GetAngle { nodeA GetCenter nodeB GetCenter 3 -1 roll sub 3 1 roll sub +neg Atan } def +/GetEdge { begin /Nodesep ED dup 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED NodePos Y add exch X add exch +NodeMtrx transform CM itransform end 4 2 roll 1 index 0 eq { pop pop } { +2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse } def +/GetPos { OffsetA AngleA NodesepA nodeA GetEdge /y1 ED /x1 ED OffsetB +AngleB NodesepB nodeB GetEdge /y2 ED /x2 ED } def +/InitNC { /nodeB ED /nodeA ED /NodesepB ED /NodesepA ED /OffsetB ED +/OffsetA ED tx@NodeDict nodeA known tx@NodeDict nodeB known and dup { +/nodeA nodeA load def /nodeB nodeB load def } if } def +/LineMP { 4 copy 1 t sub mul exch t mul add 3 1 roll 1 t sub mul exch t +mul add exch 6 2 roll sub 3 1 roll sub Atan } def +/NCCoor { GetAngle /AngleA ED /AngleB AngleA 180 add def GetPos /LPutVar +[ x2 x1 y2 y1 ] cvx def /LPutPos { LPutVar LineMP } def x1 y1 x2 y2 } +def +/NCLine { NCCoor tx@Dict begin ArrowB 4 2 roll ArrowA lineto end } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan } def +/GetArms { /x1a armA AngleA cos mul x1 add def /y1a armA AngleA sin mul +y1 add def /x2a armB AngleB cos mul x2 add def /y2a armB AngleB sin mul +y2 add def } def +/NCCurve { GetPos x1 x2 sub y1 y2 sub Pyth 2 div dup 3 -1 roll mul /armA +ED mul /armB ED GetArms x1a y1a x1 y1 tx@Dict begin ArrowA end x2a y2a +x2 y2 tx@Dict begin ArrowB end curveto /LPutVar [ x1 y1 x1a y1a x2a y2a +x2 y2 ] cvx def /LPutPos { t LPutVar BezierMidpoint } def } def +/AnglesMP { LPutVar t 3 gt { /t t 3 sub def } { t 2 gt { /t t 2 sub def +10 -2 roll } { t 1 gt { /t t 1 sub def 10 -4 roll } { 10 4 roll } ifelse +} ifelse } ifelse 6 { pop } repeat 3 -1 roll exch LineMP } def +/NCAngles { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform pop x2a y2a mtrx transform exch pop mtrx itransform /y0 ED /x0 +ED mark armB 0 ne { x2 y2 } if x2a y2a x0 y0 x1a y1a armA 0 ne { x1 y1 } +if tx@Dict begin false Line end /LPutVar [ x2 y2 x2a y2a x0 y0 x1a y1a +x1 y1 ] cvx def /LPutPos { AnglesMP } def } def +/NCAngle { GetPos /x2a armB AngleB cos mul x2 add def /y2a armB AngleB +sin mul y2 add def /mtrx AngleA matrix rotate def x2a y2a mtrx transform +pop x1 y1 mtrx transform exch pop mtrx itransform /y0 ED /x0 ED mark +armB 0 ne { x2 y2 } if x2a y2a x0 y0 x1 y1 tx@Dict begin false Line end +/LPutVar [ x2 y2 x2 y2 x2a y2a x0 y0 x1 y1 ] cvx def /LPutPos { AnglesMP +} def } def +/NCBar { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform pop x2a y2a mtrx transform pop sub dup 0 mtrx itransform 3 -1 +roll 0 gt { /y2a exch y2a add def /x2a exch x2a add def } { /y1a exch +neg y1a add def /x2a exch neg x2a add def } ifelse mark x2 y2 x2a y2a +x1a y1a x1 y1 tx@Dict begin false Line end /LPutVar [ x2 y2 x2 y2 x2a +y2a x1a y1a x1 y1 ] cvx def /LPutPos { LPutVar AnglesMP } def } def +/NCDiag { GetPos GetArms mark x2 y2 x2a y2a x1a y1a x1 y1 tx@Dict begin +false Line end /LPutVar [ x2 y2 x2 y2 x2a y2a x1a y1a x1 y1 ] cvx def +/LPutPos { AnglesMP } def } def +/NCDiagg { OffsetA AngleA NodesepA nodeA GetEdge /y1 ED /x1 ED /x1a armA +AngleA cos mul x1 add def /y1a armA AngleA sin mul y1 add def nodeB +GetCenter y1a sub exch x1a sub Atan 180 add /AngleB ED OffsetB AngleB +NodesepB nodeB GetEdge /y2 ED /x2 ED mark x2 y2 x1a y1a x1 y1 tx@Dict +begin false Line end /LPutVar [ x2 y2 x2 y2 x2 y2 x1a y1a x1 y1] cvx def +/LPutPos { AnglesMP } def } def +/LoopMP { /t t abs def [ LPutVar ] length 2 div 1 sub dup t lt { /t ED } +{ pop } ifelse mark LPutVar t cvi { /t t 1 sub def pop pop } repeat +counttomark 1 add 4 roll cleartomark 3 -1 roll exch LineMP } def +/NCLoop { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform loopsize add /y1b ED /x1b ED /x2b x2a y2a mtrx transform pop +def x2b y1b mtrx itransform /y2b ED /x2b ED x1b y1b mtrx itransform /y1b +ED /x1b ED mark armB 0 ne { x2 y2 } if x2a y2a x2b y2b x1b y1b x1a y1a +armA 0 ne { x1 y1 } if tx@Dict begin false Line end /LPutVar [ x2 y2 x2a +y2a x2b y2b x1b y1b x1a y1a x1 y1 ] cvx def /LPutPos { LoopMP } def } +def +/NCCircle { nodeA GetCenter 0 0 NodesepA nodeA GetEdge pop 3 1 roll /Y ED +/X ED X sub 2 div dup 2 exp r r mul sub abs sqrt atan 2 mul /a ED r +AngleA 90 add PtoC Y add exch X add exch 2 copy /LPutVar [ 4 2 roll r a +] def /LPutPos { LPutVar aload pop t 360 mul add dup 5 1 roll 90 sub +PtoC 3 -1 roll add 3 1 roll add exch 3 -1 roll } def r AngleA 90 sub a +add AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c +57.2957 r Div def /y ED /x ED } def +/LPutCoor { tx@NodeDict /LPutPos known { gsave LPutPos tx@Dict begin +/langle ED CM 3 1 roll STV CP 3 -1 roll sub neg 3 1 roll sub exch moveto +setmatrix CP end grestore } { 0 0 tx@Dict /langle 0 def end } ifelse } +def +end +%%EndProcSet +%%BeginProcSet: texps.pro +TeXDict begin /rf{findfont dup length 1 add dict begin{1 index /FID ne 2 +index /UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type /integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics /Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont /setfont load]cvx def}def +/ObliqueSlant{dup sin S cos div neg}B /SlantFont{4 index mul add}def +/ExtendFont{3 -1 roll mul exch}def /ReEncodeFont{/Encoding exch def}def +end +%%EndProcSet +%%BeginProcSet: special.pro +TeXDict begin /SDict 200 dict N SDict begin /@SpecialDefaults{/hs 612 N +/vs 792 N /ho 0 N /vo 0 N /hsc 1 N /vsc 1 N /ang 0 N /CLIP 0 N /rwiSeen +false N /rhiSeen false N /letter{}N /note{}N /a4{}N /legal{}N}B +/@scaleunit 100 N /@hscale{@scaleunit div /hsc X}B /@vscale{@scaleunit +div /vsc X}B /@hsize{/hs X /CLIP 1 N}B /@vsize{/vs X /CLIP 1 N}B /@clip{ +/CLIP 2 N}B /@hoffset{/ho X}B /@voffset{/vo X}B /@angle{/ang X}B /@rwi{ +10 div /rwi X /rwiSeen true N}B /@rhi{10 div /rhi X /rhiSeen true N}B +/@llx{/llx X}B /@lly{/lly X}B /@urx{/urx X}B /@ury{/ury X}B /magscale +true def end /@MacSetUp{userdict /md known{userdict /md get type +/dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup +length 20 add dict copy def}if end md begin /letter{}N /note{}N /legal{} +N /od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath +clippath mark{transform{itransform moveto}}{transform{itransform lineto} +}{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{ +itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{ +closepath}}pathforall newpath counttomark array astore /gc xdf pop ct 39 +0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if}N +/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 +scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get +ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip +not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 +TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{noflips{TR +pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 +-1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg +TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg +sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr +0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 -1 roll add +2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N /cp +{pop pop showpage pm restore}N end}if}if}N /normalscale{Resolution 72 +div VResolution 72 div neg scale magscale{DVImag dup scale}if 0 setgray} +N /psfts{S 65781.76 div N}N /startTexFig{/psf$SavedState save N userdict +maxlength dict begin /magscale false def normalscale currentpoint TR +/psf$ury psfts /psf$urx psfts /psf$lly psfts /psf$llx psfts /psf$y psfts +/psf$x psfts currentpoint /psf$cy X /psf$cx X /psf$sx psf$x psf$urx +psf$llx sub div N /psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy +scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub TR +/showpage{}N /erasepage{}N /copypage{}N /p 3 def @MacSetUp}N /doclip{ +psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 +roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath +moveto}N /endTexFig{end psf$SavedState restore}N /@beginspecial{SDict +begin /SpecialSave save N gsave normalscale currentpoint TR +@SpecialDefaults count /ocount X /dcount countdictstack N}N /@setspecial +{CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto +closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx +sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR +}{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse +CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury +lineto closepath clip}if /showpage{}N /erasepage{}N /copypage{}N newpath +}N /@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{ +end}repeat grestore SpecialSave restore end}N /@defspecial{SDict begin} +N /@fedspecial{end}B /li{lineto}B /rl{rlineto}B /rc{rcurveto}B /np{ +/SaveX currentpoint /SaveY X N 1 setlinecap newpath}N /st{stroke SaveX +SaveY moveto}N /fil{fill SaveX SaveY moveto}N /ellipse{/endangle X +/startangle X /yrad X /xrad X /savematrix matrix currentmatrix N TR xrad +yrad scale 0 0 1 startangle endangle arc savematrix setmatrix}N end +%%EndProcSet +TeXDict begin @defspecial + + TeXDict begin /box{newpath 2 copy moveto 3 copy pop exch lineto 4 +copy pop pop lineto 4 copy exch pop exch pop lineto closepath } bind +def /min{ 2 copy gt { exch } if pop } bind def/max{ 2 copy lt { exch +} if pop } bind def/roundedbox{/radius exch store 3 2 roll 2 copy min +radius sub /miny exch store max radius add /maxy exch store 2 copy +min radius sub /minx exch store max radius add /maxx exch store newpath +minx radius add miny moveto maxx miny maxx maxy radius arcto maxx maxy +minx maxy radius arcto minx maxy minx miny radius arcto minx miny maxx +miny radius arcto 16 {pop} repeat closepath }bind def /rectcartouche{box +gsave .95 setgray fill grestore 1 setlinewidth stroke }bind def /cartouche{roundedbox +gsave .95 setgray fill grestore 1 setlinewidth stroke }bind def end 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begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a -7 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 182 +415 a + tx@Dict begin 45. Rot end + 182 415 a 143 418 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 143 418 a Fl(:)10 b(:)g(:)182 +415 y + tx@Dict begin 45. neg Rot end + 182 415 a -7 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + -7 699 a 331 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 331 429 a +Fm(RET)336 520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.32748 0.99998 +false .5 8.23895 InitRnode } NewNode end end + 336 520 a Fa(C)364 528 y Fl(n)-7 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 231 335 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.39499 +0.05246 false .5 10.8299 InitRnode } NewNode end end + 231 335 a Fm(JOIN)-7 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + -7 699 +a -7 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 100 881 a Fz(\(a\))17 b(E1)p 447 +976 4 928 v 476 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + 476 707 a Fa(C)504 719 y Fn(1)467 +618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 467 618 a Fm(RET)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 665 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + +665 707 a Fa(C)693 719 y Fn(2)656 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 656 618 a Fm(RET)506 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 463 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl1 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 463 524 a Fm(MA)-5 b(T)506 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl1 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 699 a 652 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl2 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 652 524 a Fm(MA)g(T)506 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 699 a 556 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoinmatgetcl1matgetcl2 +16 { .5 3.39499 0.05246 false .5 10.8299 InitRnode } NewNode end end + 556 429 a Fm(JOIN)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 +699 a 506 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 699 a 695 321 a + tx@Dict begin 45. Rot end + 695 321 a 656 324 +a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 656 324 a Fl(:)11 b(:)f(:)695 321 y + tx@Dict begin 45. neg Rot end + 695 321 a 506 699 +a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 506 699 a 845 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 845 429 a Fm(RET)850 520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.32748 0.99998 +false .5 8.23895 InitRnode } NewNode end end + 850 +520 a Fa(C)878 528 y Fl(n)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 841 335 +a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcln 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 841 335 a Fm(MA)-5 b(T)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodematgetcln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 745 240 +a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.39499 +0.05246 false .5 10.8299 InitRnode } NewNode end end + 745 240 a Fm(JOIN)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 506 699 a 506 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodematgetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 +699 a 611 881 a Fz(\(b\))17 b(E2)p 961 976 4 928 v 990 +707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + 990 707 a Fa(C)1018 719 y Fn(1)981 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 981 618 +a Fm(RET)1020 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1179 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + 1179 707 a +Fa(C)1207 719 y Fn(2)1170 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 1170 618 a Fm(RET)1020 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1070 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoingetcl1getcl2 16 { +.5 3.39499 0.05246 false .5 10.8299 InitRnode } NewNode end end + 1070 524 a Fm(JOIN)1020 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1020 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1209 415 a + tx@Dict begin 45. Rot end + 1209 415 +a 1170 418 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 1170 418 a Fl(:)11 b(:)f(:)1209 415 y + tx@Dict begin 45. neg Rot end + 1209 +415 a 1020 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1020 699 a 1359 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 1359 429 a Fm(RET)1364 +520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.32748 0.99998 +false .5 8.23895 InitRnode } NewNode end end + 1364 520 a Fa(C)1392 528 y Fl(n)1020 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 +699 a 1259 335 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.39499 +0.05246 false .5 10.8299 InitRnode } NewNode end end + 1259 335 a Fm(JOIN)1020 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1020 699 +a 1020 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1227 240 a + tx@Dict begin tx@NodeDict begin { } /TheNodeselect 16 { .5 3.39499 +0.05246 false .5 18.3349 InitRnode } NewNode end end + 1227 240 a Fm(SELECT)1020 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodeselect +/TheNoderoot InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1020 699 a 1127 881 a Fz(\(c\))17 b(E3)p 1474 976 +4 928 v 1504 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + 1504 707 a Fa(C)1531 719 y Fn(1)1495 +618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 1495 618 a Fm(RET)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1693 707 +a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + 1693 707 a Fa(C)1720 719 y Fn(2)1684 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 1684 618 +a Fm(RET)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1490 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl1 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 1490 524 a +Fm(MA)-5 b(T)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl1 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a 1679 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl2 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 1679 524 +a Fm(MA)g(T)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a 1583 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoinmatgetcl1matgetcl2 +16 { .5 3.39499 0.05246 false .5 10.8299 InitRnode } NewNode end end + 1583 429 +a Fm(JOIN)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a 1534 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a +1723 321 a + tx@Dict begin 45. Rot end + 1723 321 a 1684 324 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 1684 324 a Fl(:)10 b(:)h(:)1723 +321 y + tx@Dict begin 45. neg Rot end + 1723 321 a 1534 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1534 699 a 1873 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 1873 +429 a Fm(RET)1878 520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.32748 0.99998 +false .5 8.23895 InitRnode } NewNode end end + 1878 520 a Fa(C)1905 528 y Fl(n)1534 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1868 335 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcln 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 1868 335 a Fm(MA)-5 b(T)1534 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodematgetcln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1772 240 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.39499 +0.05246 false .5 10.8299 InitRnode } NewNode end end + 1772 240 a Fm(JOIN)1534 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1534 699 a 1534 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodematgetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a 1741 146 a + tx@Dict begin tx@NodeDict begin { } /TheNodeselect 16 { .5 3.39499 +0.05246 false .5 18.3349 InitRnode } NewNode end end + 1741 146 +a Fm(SELECT)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodeselect +/TheNoderoot InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1534 699 a 1639 881 a Fz(\(d\))17 +b(E4)p 2014 1001 4 978 v -112 1004 2130 4 v 2015 1021 +19 984 v -96 1021 2130 19 v -112 1204 a FG(Figure)g(6:)26 +b(Expressions)17 b(used)h(in)g(generating)e(queries)i(for)f +(experiments)p 2359 357 1644 13 v 2359 423 4 67 v 2412 +437 a Fp(Query)p 2620 423 V 2673 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FG(,)i(25\(2\):73\261170,)2224 +2445 y(June)20 b(1993.)2085 2611 y([9])41 b(Goetz)29 +b(Graefe)h(and)f(David)g(J.)i(DeW)m(itt.)78 b(The)30 +b(EXODUS)2224 2710 y(optimizer)21 b(generator)-5 b(.)42 +b(In)23 b FF(Pr)m(oceedings)e(1987)h(ACM)i(SIG-)2224 +2810 y(MOD)40 b(International)d(Confer)m(ence)i(on)g(Management)f(of) +2224 2910 y(Data)p FG(,)19 b(pages)h(387\261394,)d(San)j(Francisco,)g +(May)g(1987.)2044 3076 y([10])40 b(L.)23 b(M.)g(Haas,)h(J.)g(C.)g +(Freytag,)e(G.)i(M.)f(Lohman,)f(and)g(H.)i(Pi-)2224 3175 +y(rahesh.)31 b(Extensible)20 b(query)f(processing)h(in)h(Starburst.)32 +b(Re-)2224 3275 y(search)20 b(Report)g(RJ)i(6610,)e(IBM)h(Almaden)e +(Research)i(Cen-)2224 3375 y(ter)m(,)e(December)g(1988.)2047 +3541 y([1)m(1])40 b(P)-9 b(.)33 b(G.)g(Selinger)m(,)h(M.)f(M.)g +(Astrahan,)i(D.)e(D.)g(Chamberlin,)2224 3640 y(R.)28 +b(A.)h(Lorie,)g(and)f(T)-6 b(.)28 b(G.)g(Price.)69 b(Access)29 +b(path)e(selection)2224 3740 y(in)d(a)g(relational)f(database)g +(management)f(system.)47 b(In)23 b FF(Pr)m(o-)2224 3840 +y(ceedings)k(1979)g(ACM)i(SIGMOD)f(International)e(Confer)n(-)2224 +3939 y(ence)g(on)h(Management)e(of)i(Data)p FG(,)h(pages)e(23\26134,)g +(Boston,)2224 4039 y(May)20 b(1979.)2044 4205 y([12])40 +b(Michael)30 b(Stonebraker)f(and)i(Lawrence)f(A.)i(Rowe.)84 +b(The)2224 4305 y(design)25 b(of)h(Postgres.)60 b(In)26 +b FF(Pr)m(oceedings)f(1986)g(ACM)i(SIG-)2224 4404 y(MOD)40 +b(International)d(Confer)m(ence)i(on)g(Management)f(of)2224 +4504 y(Data)p FG(,)19 b(pages)h(340\261355,)d(W)-7 b(ashington,)19 +b(May)h(1986.)p eop +%%Trailer +end +userdict /end-hook known{end-hook}if +%%EOF diff --git a/macros/latex/contrib/utthesis/ICDE-11/results.tex b/macros/latex/contrib/utthesis/ICDE-11/results.tex new file mode 100644 index 0000000000..d9ae183329 --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/results.tex @@ -0,0 +1,473 @@ +\section{Experimental results} +\label{sec:results} + +This section presents experimental results which demonstrate the value +of Prairie in specifying rule sets of rule-based optimizers. Our +experiments consist of specifying rule-based optimizers using Prairie +and generating optimizers using the P2V pre-processor and the +optimizer-generator paradigm of Figure~\ref{fig:ptovmodel}. + +In \cite{Das93}, we presented an implementation of a centralized +relational query optimizer using Prairie. Using the P2V translator, we +translated this to Volcano format and optimized several queries using +the resultant optimizer. For comparison, we hand-coded the same +optimizer directly in Volcano. The results presented there showed +that, using Prairie (compared to directly using Volcano) resulted in +approximately 50\% savings in lines of code with negligible (less than +5\%) increase in query optimization time. However, the optimizer was +quite small in terms of the number of operators, algorithms and rules. + +For a more realistic evaluation of Prairie, we needed answers to +the following questions: +\begin{enumerate} +\item Is Prairie adequate for large-scale rule sets? +\item How is programmer productivity enhanced by the high-level + abstractions of Prairie? +\item Can Prairie rule sets be translated automatically into + efficient implementations? +\end{enumerate} + +We addressed the first question by using the Texas Instruments Open +OODB query optimizer rule set, which has the largest publicly +available rule set. We describe this optimizer in the next section, +and then give our assessments to the last two questions in subsequent +sections. + +\subsection{The Texas Instruments Open OODB query optimizer} +\label{sec:oodb} + +The Texas Instruments Open Object-Oriented Database Management System +is an open, extensible, object-oriented database system which provides +users an architectural framework that is configurable in an incremental +manner. The query optimizer in the Open OODB \cite{Blak93} is +generated using Volcano. It is written as a set of trans\_rules and +impl\_rules that define the algebra of an object-oriented database +system. Currently, there are 17 transformation rules and 9 +implementation rules together with about $13,000$ lines of code for +support functions; this, of course, can be changed by an Open OODB user +for specific needs. + +\subsection{Programmer productivity} +\label{sec:productivity} + +Programmer productivity can be measured in different ways. An +admittedly simplistic metric is the number of lines of code that must +be written. But there are also less tangible measures, such as the +amount of conceptual effort needed to understand a particular +programming task. Our experience with the Open OODB query optimizer +suggests that Prairie excels on the latter, while offering modest +reductions in the volume of code that needs to be written. + +We converted by hand the Open OODB query optimizer's Volcano +specifications to Prairie. This was a non-trivial task because of the +relatively large size of the rule set and the complexity of the support +functions. This was where we found Prairie helped in conceptually +simplifying the rules and actions. We then used our P2V pre-processor +to reconstitute these Prairie specifications as Volcano +specifications. As described in Section~\ref{sec:ptov}, this process +involved a considerable level of complexity, partly because the Prairie +specification had 22 T-rules and 11 I-rules compared to 17 trans\_rules +and 9 impl\_rules in the Volcano specification; the reconstituted +Volcano specification had the same number of trans\_rules and +impl\_rules as the original hand-coded specification. + +Converting the Open OODB optimizer rule set into Prairie format +actually simplified its specification as the complexities of the +Volcano model were removed. The reduction in lines of code was modest +--- there was about a 10\% savings.\footnote{The original Volcano +specification had $13,400$ lines, the Prairie specification had +$12,100$ lines, and the P2V-generated Volcano specification had +$15,800$ lines.} However, as mentioned above, savings in lines of code +do not adequately reflect increases in programmer productivity. We +found the encapsulated specifications of Prairie --- namely, the use of +a single descriptor and fewer explicit support functions --- made rule +programming \emph{much} easier. + +\subsection{Performance results using the Open OODB optimizer} +\label{sec:oodbexp} + +\newsavebox{\Eone} +\newsavebox{\Etwo} +\newsavebox{\Ethree} +\newsavebox{\Efour} + +\begin{lrbox}{\Eone} +\begin{minipage}[b]{1.9cm} +\psset{unit=4mm} +\psset{nodesep=1pt} +\tiny +\begin{center} +\begin{pspicture}(0,0)(4,4) +\rput(0,0){\rnode{cl1}{$\textit{C}_1$}} +\rput(0,1){\rnode{getcl1}{RET}} +\ncline{-}{cl1}{getcl1} +\rput(2,0){\rnode{cl2}{$\textit{C}_2$}} +\rput(2,1){\rnode{getcl2}{RET}} +\ncline{-}{cl2}{getcl2} +\rput(1,2){\rnode{joingetcl1getcl2}{JOIN}} +\ncline{-}{joingetcl1getcl2}{getcl1} +\ncline{-}{joingetcl1getcl2}{getcl2} +\rput{45}(2,3){\rnode{dots}{$\ldots$}} +\ncline{-}{joingetcl1getcl2}{dots} +\rput(4,3){\rnode{getcln}{RET}} +\rput(4,2){\rnode{cln}{$\textit{C}_n$}} +\ncline{-}{cln}{getcln} +\rput(3,4){\rnode{root}{JOIN}} +\ncline{-}{root}{dots} +\ncline{-}{root}{getcln} +\end{pspicture} +\end{center} +\end{minipage} +\end{lrbox} + +\begin{lrbox}{\Etwo} +\begin{minipage}[b]{1.9cm} +\psset{unit=4mm} +\psset{nodesep=1pt} +\tiny +\begin{center} +\begin{pspicture}(0,0)(4,5) +\rput(0,0){\rnode{cl1}{$\textit{C}_1$}} +\rput(0,1){\rnode{getcl1}{RET}} +\ncline{-}{cl1}{getcl1} +\rput(2,0){\rnode{cl2}{$\textit{C}_2$}} +\rput(2,1){\rnode{getcl2}{RET}} +\ncline{-}{cl2}{getcl2} +\rput(0,2){\rnode{matgetcl1}{MAT}} +\ncline{-}{getcl1}{matgetcl1} +\rput(2,2){\rnode{matgetcl2}{MAT}} +\ncline{-}{getcl2}{matgetcl2} +\rput(1,3){\rnode{joinmatgetcl1matgetcl2}{JOIN}} +\ncline{-}{joinmatgetcl1matgetcl2}{matgetcl1} +\ncline{-}{joinmatgetcl1matgetcl2}{matgetcl2} +\rput{45}(2,4){\rnode{dots}{$\ldots$}} +\ncline{-}{joinmatgetcl1matgetcl2}{dots} +\rput(4,3){\rnode{getcln}{RET}} +\rput(4,2){\rnode{cln}{$\textit{C}_n$}} +\ncline{-}{cln}{getcln} +\rput(4,4){\rnode{matgetcln}{MAT}} +\ncline{-}{matgetcln}{getcln} +\rput(3,5){\rnode{root}{JOIN}} +\ncline{-}{root}{dots} +\ncline{-}{root}{matgetcln} +\end{pspicture} +\end{center} +\end{minipage} +\end{lrbox} + +\begin{lrbox}{\Ethree} +\begin{minipage}[b]{1.9cm} +\psset{unit=4mm} +\psset{nodesep=1pt} +\tiny +\begin{center} +\begin{pspicture}(0,0)(4,5) +\rput(0,0){\rnode{cl1}{$\textit{C}_1$}} +\rput(0,1){\rnode{getcl1}{RET}} +\ncline{-}{cl1}{getcl1} +\rput(2,0){\rnode{cl2}{$\textit{C}_2$}} +\rput(2,1){\rnode{getcl2}{RET}} +\ncline{-}{cl2}{getcl2} +\rput(1,2){\rnode{joingetcl1getcl2}{JOIN}} +\ncline{-}{joingetcl1getcl2}{getcl1} +\ncline{-}{joingetcl1getcl2}{getcl2} +\rput{45}(2,3){\rnode{dots}{$\ldots$}} +\ncline{-}{joingetcl1getcl2}{dots} +\rput(4,3){\rnode{getcln}{RET}} +\rput(4,2){\rnode{cln}{$\textit{C}_n$}} +\ncline{-}{cln}{getcln} +\rput(3,4){\rnode{root}{JOIN}} +\ncline{-}{root}{dots} +\ncline{-}{root}{getcln} +\rput(3,5){\rnode{select}{SELECT}} +\ncline{-}{select}{root} +\end{pspicture} +\end{center} +\end{minipage} +\end{lrbox} + +\begin{lrbox}{\Efour} +\begin{minipage}[b]{1.9cm} +\psset{unit=4mm} +\psset{nodesep=1pt} +\tiny +\begin{center} +\begin{pspicture}(0,0)(4,6) +\rput(0,0){\rnode{cl1}{$\textit{C}_1$}} +\rput(0,1){\rnode{getcl1}{RET}} +\ncline{-}{cl1}{getcl1} +\rput(2,0){\rnode{cl2}{$\textit{C}_2$}} +\rput(2,1){\rnode{getcl2}{RET}} +\ncline{-}{cl2}{getcl2} +\rput(0,2){\rnode{matgetcl1}{MAT}} +\ncline{-}{getcl1}{matgetcl1} +\rput(2,2){\rnode{matgetcl2}{MAT}} +\ncline{-}{getcl2}{matgetcl2} +\rput(1,3){\rnode{joinmatgetcl1matgetcl2}{JOIN}} +\ncline{-}{joinmatgetcl1matgetcl2}{matgetcl1} +\ncline{-}{joinmatgetcl1matgetcl2}{matgetcl2} +\rput{45}(2,4){\rnode{dots}{$\ldots$}} +\ncline{-}{joinmatgetcl1matgetcl2}{dots} +\rput(4,3){\rnode{getcln}{RET}} +\rput(4,2){\rnode{cln}{$\textit{C}_n$}} +\ncline{-}{cln}{getcln} +\rput(4,4){\rnode{matgetcln}{MAT}} +\ncline{-}{matgetcln}{getcln} +\rput(3,5){\rnode{root}{JOIN}} +\ncline{-}{root}{dots} +\ncline{-}{root}{matgetcln} +\rput(3,6){\rnode{select}{SELECT}} +\ncline{-}{select}{root} +\end{pspicture} +\end{center} +\end{minipage} +\end{lrbox} + +\begin{centeredfigure*} +\begin{minipage}[b]{9.1cm} +\myshadowbox{ +\begin{minipage}[b]{8.6cm} +\subfigure[E1] { \usebox{\Eone} \label{fig:Eone} } +\vrule +\subfigure[E2] { \usebox{\Etwo} \label{fig:Etwo} } +\vrule +\subfigure[E3] { \usebox{\Ethree} \label{fig:Ethree} } +\vrule +\subfigure[E4] { \usebox{\Efour} \label{fig:Efour} } +\normalsize +\end{minipage} +} +\caption{Expressions used in generating queries for experiments} +\label{fig:exps} +\end{minipage} +\hfill +\begin{minipage}[b]{7.0cm} +% Save current figure counter +\newcounter{savectr} +\setcounter{savectr}{\value{figure}} +% Temporarily change the figure to a table. +\renewcommand{\figurename}{\tablename} +\setcounter{figure}{\value{table}} +\scriptsize +\renewcommand{\multirowsetup}{\centering} +\newlength{\Lone} +\settowidth{\Lone}{E4} +\newlength{\Ltwo} +\settowidth{\Ltwo}{\textbf{Query}} +\newlength{\Lthree} +\settowidth{\Lthree}{\textbf{Indices?}} +\newlength{\Lfour} +\settowidth{\Lfour}{\textbf{Expression}} +\newlength{\Lnum} +\settowidth{\Lnum}{99} +\begin{tabular}{|c|c|c|c|c|} \thickhline +\multirow{2}{\Ltwo}{\textbf{Query}} + & \multirow{2}{\Lthree}{\textbf{Indices?}} + & \multirow{2}{\Lfour}{\textbf{Expression}} + & \multicolumn{2}{c|}{\textbf{Rules matched}} \\ \cline{4-5} +& & & trans\_rules & impl\_rules \\ \thickhline +Q1 & No & \multirow{2}{\Lone}{E1} & \multirow{2}{\Lnum}{3} + & \multirow{2}{\Lnum}{3} \\ \cline{1-2} +Q2 & Yes & & & \\ \hline +Q3 & No & \multirow{2}{\Lone}{E2} & \multirow{2}{\Lnum}{8} + & \multirow{2}{\Lnum}{4} \\ \cline{1-2} +Q4 & Yes & & & \\ \hline +Q5 & No & \multirow{2}{\Lone}{E3} & \multirow{2}{\Lnum}{9} + & \multirow{2}{\Lnum}{5} \\ \cline{1-2} +Q6 & Yes & & & \\ \hline +Q7 & No & \multirow{2}{\Lone}{E4} & \multirow{2}{\Lnum}{16} + & \multirow{2}{\Lnum}{7} \\ \cline{1-2} +Q8 & Yes & & & \\ \thickhline +\end{tabular} +\caption{Queries used in experiments} +\label{tab:queries} +% Change figure back as usual. +\renewcommand{\figurename}{Figure} +\setcounter{figure}{\value{savectr}} +\end{minipage} +\end{centeredfigure*} + +The acid test of Prairie was whether Prairie specifications could be +translated into efficient optimizer implementations. Our experiments +using the Open OODB consisted of optimizing 8 different queries using +the two query optimizers generated, respectively, using Prairie and +using Volcano directly (in the remainder of this section, we will use +``Prairie'' and ``Volcano'' to denote these two approaches). There +were 4 distinct expressions that were used to generate the queries used +in the experiments; these are shown in Figure~\ref{fig:exps}. Each +expression represents an $N$-way join query for varying $N$. + +The first expression E1 is a simple retrieval and join of base +classes. The second, E2, is also a join of base classes; however, +after each class retrieval, an attribute has to be materialized (\ie +brought into view) before the join. The third and fourth expressions +(E3 and E4) are the same as the first and second (E1 and E2) +respectively, except that there is a selection of attributes (the +select operator is the root of the expressions).\footnote{ The most +complex expression E4 consists of all operators in the algebra, except +PROJECT and UNNEST. PROJECT was not considered because it appeared in +only one impl\_rule and no trans\_rules, and thus, would not affect the +size of the search space of abstract expressions. UNNEST was not +considered because it appeared in exactly one trans\_rule and one +impl\_rule; including it in our queries would have increased the number +of parameters that could affect our run-times. We preferred to +concentrate on simple JOIN expressions.} + +The algebra that was used in the Prairie and Volcano optimizers for our +experiments consisted of 5 relational operators SELECT, PROJECT, JOIN, +RET and UNNEST (for set-valued attributes) and an object-oriented +operator called MAT (for MATerialize; it is fundamentally a +pointer-chasing operator for attributes of a class). There were 8 +algorithms. + +There are many parameters that can be varied when benchmarking a query +optimizer. Since our objective was to verify that the Prairie approach +did not sacrifice efficiency, our criteria for the queries was that +they test a majority of the rules, with varying properties of the base +classes. To this end, we tested our optimizer (and the Volcano +optimizer) with 8 different queries (shown in Table~\ref{tab:queries}). +The eight queries Q1 through Q8 are derived from the 4 expressions in +Figure~\ref{fig:exps}. Each expression E1 through E4 is used to obtain +two queries for a fixed number $N$ of JOINs in the expression. The +only difference between the two queries obtained from an expression is +that the first one does not contain any indices on any classes, whereas +the second one contains a single index on each base class occurring in +the expression. In expressions where a SELECT is present (E3 and E4), +the selection predicate is a conjunction of equality predicates +$\textit{bc}_i == \textit{const}_i$, where $\textit{bc}_i$ is an +attribute of class $\textit{C}_i$, and $\textit{const}_i$ is a constant +(we arbitrarily set this to $i$, because its value doesn't affect the +correctness or performance of the optimizer). In addition, for queries +with a SELECT and whose base classes have indices (Q6 and Q8 in +Table~\ref{tab:queries}), the (single) index of each base class was +chosen to be the attribute referenced in the selection predicate. For +example, class $\textit{C}_i$ was chosen to have an index on attribute +$\textit{bc}_i$. The join predicates for each JOIN were chosen at +random, and were always equality predicates. The choice of JOIN +predicates was such that the queries corresponded to linear query +graphs. In the future, we will experiment with non-linear (\eg star) +query graphs. + +Table~\ref{tab:queries} also shows the number of trans\_rules and +impl\_rules that are matched by each expression. These are the rules +whose left hand sides match a sub-expression. However, not all the +rules were necessarily applicable. For instance, an impl\_rule with an +index scan would not apply to Q3, although it might apply to Q4. + +Queries Q1 through Q8 were optimized for increasing number $N$ of +JOINs. For a fixed number of JOINs in a query, we varied the +cardinalities of the base classes 5 times, each time generating a query +with different class properties, and averaged the run-times over the 5 +query instances to generate the per-query optimization time. Thus, +each point in our graphs represents the average of 5 queries. The +run-times were measured\footnote{Since the run-times were too small to +be measured accurately with \texttt{time}, each query instance was +optimized 3000 times (in a loop) and the total time was divided by 3000 +to get the per-query optimization time.} using the GNU \texttt{time} +command. All experiments were performed on a lightly loaded DECstation +5000/200 running Ultrix 4.2. + +The optimization times for each query for both approaches (Prairie and +Volcano) are shown in Figures~\ref{fig:q1} through \ref{fig:q8}. The +number of joins in each set of graphs was varied to a maximum of 8, or +until virtual memory was exhausted. + +The first set of graphs (Figures~\ref{fig:q1} and \ref{fig:q2}) +shows the performance of a simple relational-type query. The +optimization times are almost identical between Prairie and Volcano, +and the notable point is that the presence of an index does not change +the optimizer's behavior, \ie the two graphs are identical. This +arises because the optimizer algebra had only two join algorithms +(pointer join and hash join), neither of which makes use of any +indices. + +The second set of graphs (Figures~\ref{fig:q3} and \ref{fig:q4}) shows +the results of optimizing Q3 and Q4. Here, as in Figures~\ref{fig:q1} +and \ref{fig:q2}, the presence (or absence) of indices makes no +difference. Both the Prairie and Volcano approaches have comparable +run-times. The sharp jump in the graphs from 7-way to 8-way joins is +due to the fact that since all optimization is done in main memory, +dynamic memory allocation (caused by \texttt{malloc} calls) results in +a lot of thrashing at this point. We speculate that in systems with +more virtual memory, the graphs will be smoother. + +The third and fourth sets of graphs in Figures~\ref{fig:q5} through +\ref{fig:q8} are optimizations of queries with a selection predicate. +In these cases, the presence of an index makes a difference if the +index is referenced in the selection predicate (as we designed). Also, +in these two figures, the performance of both Prairie and Volcano was +almost identical, except that Prairie does slightly worse due to the +larger number of \texttt{malloc} calls that the P2V translator +introduces. Also, note that we could only go up to 3-way joins before +virtual memory was exhausted. As the available memory decreases, there +is increased thrashing (as shown by the sharp changes in slope in the +plots) resulting in a much slower optimization process. + +\begin{centeredfigure} +\myshadowbox +{ +\setlength{\tabcolsep}{0pt} +\begin{tabular}{ll} +\subfigure[Query 1] { \begin{centeredinhalfminipage} + \vspace{3mm} + \epsfig{file=runtime_Q1.ps,width=3.0cm} + \end{centeredinhalfminipage} + \label{fig:q1} } +& +\subfigure[Query 2] { \begin{centeredinhalfminipage} + \vspace{3mm} + \epsfig{file=runtime_Q2.ps,width=3.0cm} + \end{centeredinhalfminipage} + \label{fig:q2} } +\\ \hline +\subfigure[Query 3] { \begin{centeredinhalfminipage} + \vspace{4mm} + \epsfig{file=runtime_Q3.ps,width=3.0cm} + \end{centeredinhalfminipage} + \label{fig:q3} } +& +\subfigure[Query 4] { \begin{centeredinhalfminipage} + \vspace{4mm} + \epsfig{file=runtime_Q4.ps,width=3.0cm} + \end{centeredinhalfminipage} + \label{fig:q4} } +\\ \hline +\subfigure[Query 5] { \begin{centeredinhalfminipage} + \vspace{4mm} + \epsfig{file=runtime_Q5.ps,width=3.0cm} + \end{centeredinhalfminipage} + \label{fig:q5} } +& +\subfigure[Query 6] { \begin{centeredinhalfminipage} + \vspace{4mm} + \epsfig{file=runtime_Q6.ps,width=3.0cm} + \end{centeredinhalfminipage} + \label{fig:q6} } +\\ \hline +\subfigure[Query 7] { \begin{centeredinhalfminipage} + \vspace{4mm} + \epsfig{file=runtime_Q7.ps,width=3.0cm} + \end{centeredinhalfminipage} + \label{fig:q7} } +& +\subfigure[Query 8] { \begin{centeredinhalfminipage} + \vspace{4mm} + \epsfig{file=runtime_Q8.ps,width=3.0cm} + \end{centeredinhalfminipage} + \label{fig:q8} } +\end{tabular} +} +\caption{Query optimization times for Q1 through Q8} +\label{fig:e4} +\end{centeredfigure} + +In all four sets of plots, we can see that Prairie performs with almost +(less than $5\%$ variation) the same efficiency as Volcano. In extreme +cases, when memory is scarce, Prairie runs more slowly (about $15\%$) +(\eg Figure~\ref{fig:q6}), but we believe that this situation already +represents a serious bottleneck for both Volcano and Prairie. + +The results presented in this section show that Prairie optimizers +need not sacrifice efficiency for clarity, even for large rule sets. +More research and validation is necessary to verify that Prairie is +an efficient tool for optimizer specification. diff --git a/macros/latex/contrib/utthesis/ICDE-11/runtime_Q1.ps b/macros/latex/contrib/utthesis/ICDE-11/runtime_Q1.ps new file mode 100644 index 0000000000..3d1d8e2ff0 --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/runtime_Q1.ps @@ -0,0 +1,519 @@ +%!PS-Adobe-2.0 EPSF-1.2 +%%BoundingBox: 50 50 500 375 +%%Creator: ACE/gr (xmgr) v2.10 +%%Title: runtime.Q1.ps +%%EndComments +/m {moveto} bind def +/l {lineto} bind def +/RJ { + stringwidth neg exch neg exch + rmoveto +} bind def +/CS { + stringwidth + 2 div neg exch 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