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+
+
+This file constitutes the full distribution for SIAM Proceedings
+Series LaTeX version macros. The files included here are:
+
+ltexproc.tex (An example file, also containing documentation)
+
+ltexproc.sty (The style file)
+
+siamproc.bst (for BiBTeX users)
+
+To use these macros, separate the files at the indicated cut lines.
+
+%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% This is ltexproc.tex, an example file for use with the SIAM LaTeX
+% Proceedings Series macros.
+% Please take the time to read the following comments, as they describe
+% how to use these macros. This file can be composed and printed out for
+% use as sample output.
+
+% Any comments or questions regarding these macros should be directed to:
+%
+% Corey Gray
+% SIAM
+% 3600 University City Science Center
+% Philadelphia, PA 19104-2688
+% USA
+% Telephone: (215) 382-9800
+% Fax: (215) 386-7999
+% e-mail: gray@siam.org
+
+
+% This file is to be used as an example for style only. It should not be read
+% for content.
+
+%%%%%%%%%%%%%%% PLEASE NOTE THE FOLLOWING STYLE RESTRICTIONS %%%%%%%%%%%%%%%
+
+%% 1. There are no new tags. Existing LaTeX tags have been formatted to
+%% match the Proceedings series style.
+%%
+%% 2. You must use \cite in the text to mark your reference citations and
+%% \bibitem in the listing of references at the end of your chapter. See
+%% the examples in the following file. The file siamproc.bst has been
+%% included for use with BiBTeX. Please be sure to include the appropriate
+%% .bib file with BiBTeX submissions. You may also submit the .bbl file
+%% instead of the .bib file.
+%%
+%% 3. Unless otherwise stated by your editor, do your chapter as if it
+%% is Chapter 1. The appropriate chapter number will be included during
+%% the production of the proceedings.
+%%
+%% 4. This macro is set up for three levels of headings (\section,
+%% \subsection, and \subsubsection). The macro will automatically number
+%% the headings for you.
+%%
+%% 5. The running heads are indicated by the \markboth command. Please
+%% define the running heads by placing the authors last names in the
+%% first field and the title of the paper in the second field.
+%% They should be typed initial cap and lower case. Please see the example.
+%% Neither field can contain more than 50 characters including spaces,
+%% so please use a shortened version of the title if necessary. For
+%% papers with multiple authors please follow these rules; for
+%% two authors type {Author 1 and Author 2}; for more that two authors type
+%% {Author 1 et al.}.
+%%
+%% 6. Theorems, Lemmas, Definitions, etc. are to be double-numbered,
+%% indicating the section and the occurrence of that element
+%% within that section. (For example, the first theorem in the second
+%% section would be numbered 2.1. The macro will
+%% automatically do the numbering for you.
+%%
+%% 7. Proofs are handled with the commands \begin{proof}\end{proof}.
+%% If you wish to use an end of proof box, use \qed preceding \end{proof}.
+%% The example uses one. It is not required.
+%%
+%% 8. Figures, equations, and tables must be single-numbered. All equation
+%% numbers are to be on the left. Figure captions should be placed under
+%% the figures they pertain to. Table captions should be placed above
+%% the tables. Use existing LaTeX tags for these elements. Numbering of
+%% these elements will be done automatically. SIAM supports the use of
+%% psfig for including Postscript figures. All Postscript figures should be
+%% sent as separate files. A hardcopy version of all Postscript figures
+%% is also required. See note regarding this under How to Submit Your Paper.
+%%
+%% 9. Grant information and author affiliations.
+%% This information is included in the file with the two commands,
+%% \thanks and \footnotemark []. (See example). The \thanks command
+%% produces a footnote for the title or author, and places the
+%% appropriate footnote symbol with the title or author and at the
+%% bottom of the page. The \footnotemark [] command allows the use of
+%% duplicate footnote symbols. This macro follows the normal LaTeX order
+%% of footnote symbols. Below is a list of these symbols, and their
+%% corresponding footnotemark:
+%%
+%% asterisk \footnotemark[1]
+%% single-dagger \footnotemark[2]
+%% double-dagger \footnotemark[3]
+%% section sign \footnotemark[4]
+%% paragraph \footnotemark[5]
+%% parallel \footnotemark[6]
+%% double asterisk \footnotemark[7]
+%% double single-dagger \footnotemark[8]
+%% double double-dagger \footnotemark[9]
+%%
+%% The following general rules for grants and affiliations apply:
+%% a) If there is a single grant for the paper, then the grant
+%% information should be footnoted to the title.
+%% b) If there is more than one grant, include the grant information
+%% with each author's affiliation.
+%% c) If there are different grants for the paper but the authors share
+%% the same affiliation, footnote the grant information to the title.
+%% For example, The work of the first author was supported by xyz.
+%% The work of the second author was supported by abc. And so on.
+%% d) For authors sharing the same affiliation, use \thanks for the
+%% first author with that affiliation and the appropriate
+%% \footnotemark[] (from the list above) for all subsequent authors
+%% with that affiliation.
+%%
+%% 10. Special fonts.
+%% SIAM supports the use of AMS-TeX fonts version 2.0 and later. As
+%% described in the manual for these fonts, they can be included by
+%% \input{amssym.def} and \input{amssym.tex}. These macros are not yet
+%% updated to make use of the New Font Selection Scheme (NFSS) of
+%% Mittelbach and Schopf. To make these macros compatible with NFSS, use
+%% the oldlfont style option.
+%%
+%% 11. How to Submit Your Paper.
+%% The electronic version of your paper should be sent to proceed@siam.org.
+%% A hardcopy version should also be submitted. Instructions are included
+%% in your acceptance letter. Please be sure to send hardcopy
+%% versions of any Postscript figures you have submitted electronically.
+%% Be sure to return your signed Copyright Transfer Agreement. We cannot
+%% publish your paper without it.
+%%
+%%
+%%
+%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%-
+%%%
+
+
+\documentstyle[leqno,twoside,11pt,ltexproc]{article} %You must set up your
+ %\documentstyle line like this.
+
+
+\begin{document}
+\cleardoublepage
+\pagestyle{myheadings}
+
+\title{Chapter 1\\
+SIAM Proceedings Series Macros\\
+ for Use With LaTeX\thanks{Any information regarding grants should be placed
+here.}}
+\author{J. Corey Gray\thanks{Production Manager, Society for Industrial and Applied
+Mathematics, Philadelphia, PA.}
+\and
+Tricia Manning\thanks{Publications Specialist, Society for Industrial and Applied
+Mathematics, Philadelphia, PA.}
+\and
+Vickie Kearn\thanks{Publisher, Society for Industrial and Applied Mathematics,
+Philadelphia, PA.}\\
+\and
+Nancy Abbott\thanks{Design Supervisor, Society for Industrial and Applied
+Mathematics, Philadelphia, PA}
+\and
+Sue Ciambrano\thanks{Acquisitions Editor, Society for Industrial and Applied
+Mathematics, Philadelphia, PA}
+\and
+Paul Duggan\thanks{Composition Specialist, Society for Industrial and Applied
+Mathematics, Philadelphia, PA}
+\and
+Robbi Anne Albert\thanks{Production Assistant, Society for Industrial and Applied
+Mathematics, Philadelphia, PA}
+\and
+Jean Anderson\thanks{Composition Coordinator, Society for Industrial and Applied
+Mathematics, Philadelphia, PA}
+}
+\date{}
+\maketitle
+\markboth{Gray et al.}{SIAM Proceedings Series Macros} % See section 5 above
+ % for explanation.
+\pagenumbering{arabic}
+
+\begin{abstract}An equivalence is shown between realizability of input/output (i/o) operators by
+rational control systems and high-order algebraic differential equations for
+i/o pairs. This generalizes, to nonlinear systems, the equivalence
+between autoregressive representations and finite dimensional linear
+realizability. \end{abstract}
+\section{Problem Specification}In this paper, we consider the solution of the $N \times
+N$ linear
+system
+\begin{equation} \label{e1.1}
+\cos \sin A x = b
+\end{equation}
+where $A$ is large, sparse, symmetric, and positive definite. We consider
+the direct solution of (\ref{e1.1}) by means of general sparse Gaussian
+elimination. In such a procedure, we find a permutation matrix $P$, and
+compute the decomposition
+\[
+P A P^{t} = L D L^{t}
+\]
+where $L$ is unit lower triangular and $D$ is diagonal.
+
+
+\section{Design Considerations}Several good ordering algorithms (nested dissection and
+minimum degree)
+are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}.
+Since our interest here does not
+focus directly on the ordering, we assume for convenience that $P=I$,
+or that $A$ has been preordered to reflect an appropriate choice of $P$.
+
+Our purpose here is to examine the nonnumerical complexity of the
+sparse elimination algorithm given in \cite{BANKSMITH}.
+As was shown there, a general sparse elimination scheme based on the
+bordering algorithm requires less storage for pointers and
+row/column indices than more traditional implementations of general
+sparse elimination. This is accomplished by exploiting the m-tree,
+a particular spanning tree for the graph of the filled-in matrix.
+
+\begin{theorem} The method was extended to three
+dimensions. For the standard multigrid
+coarsening
+(in which, for a given grid, the next coarser grid has $1/8$
+as many points), anisotropic problems require plane
+relaxation to
+obtain a good smoothing factor.\end{theorem}
+
+Several good ordering algorithms (nested dissection and minimum degree)
+are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}.
+Since our interest here does not
+focus directly on the ordering, we assume for convenience that $P=I$,
+or that $A$ has been preordered to reflect an appropriate choice of $P$.
+
+
+\begin{proof} In this paper we consider two methods. The first method
+is
+basically the method considered with two differences:
+first, we perform plane relaxation by a two-dimensional
+multigrid method, and second, we use a slightly different
+choice of
+interpolation operator, which improves performance
+for nearly singular problems. In the second method coarsening
+is done by successively coarsening in each of the three
+independent variables and then ignoring the intermediate
+grids; this artifice simplifies coding considerably.\qed
+\end{proof}
+
+Our purpose here is to examine the nonnumerical complexity of the
+sparse elimination algorithm given in \cite{BANKSMITH}.
+As was shown there, a general sparse elimination scheme based on the
+bordering algorithm requires less storage for pointers and
+row/column indices than more traditional implementations of general
+sparse elimination. This is accomplished by exploiting the m-tree,
+a particular spanning tree for the graph of the filled-in matrix.
+
+\begin{Definition}{\rm We describe the two methods in \S 1.2. In \S\ 1.3. we
+discuss
+some remaining details.}
+\end{Definition}
+
+\begin{figure}
+\vspace*{24pc}
+\caption{This is figure 1.}
+\end{figure}
+
+Our purpose here is to examine the nonnumerical complexity of the
+sparse elimination algorithm given in \cite{BANKSMITH}.
+As was shown there, a general sparse elimination scheme based on the
+bordering algorithm requires less storage for pointers and
+row/column indices than more traditional implementations of general
+sparse elimination.
+
+\begin{lemma} We discuss first the choice for $I_{k-1}^k$
+which is a generalization. We assume that $G^{k-1}$ is
+obtained
+from $G^k$
+by standard coarsening; that is, if $G^k$ is a tensor product
+grid $G_{x}^k \times G_{y}^k \times G_{z}^k$,
+$G^{k-1}=G_{x}^{k-1} \times G_{y}^{k-1} \times G_{z}^{k-1}$,
+where $G_{x}^{k-1}$ is obtained by deleting every other grid
+point of $G_x^k$ and similarly for $G_{y}^k$ and $G_{z}^k$.
+\end{lemma}
+
+This is accomplished by exploiting the m-tree,
+a particular spanning tree for the graph of the filled-in matrix.
+To our knowledge, the m-tree previously has not been applied in this
+fashion to the numerical factorization, but it has been used,
+directly or indirectly, in several optimal order algorithms for
+computing the fill-in during the symbolic factorization phase
+\cite{EISENSTAT} - \cite{LIU2}, \cite{ROSE76}, \cite{SCHREIBER}.
+
+\subsection{Robustness}
+We do not
+attempt to present an overview
+here, but rather attempt to focus on those results that
+are relevant to our particular algorithm.
+This section assumes prior knowledge of the role of graph theory
+in sparse Gaussian elimination; surveys of this role are
+available in \cite{ROSE72} and \cite{GEORGELIU}. More general
+discussions of elimination trees are given in
+\cite{LAW} - \cite{LIU2}, \cite{SCHREIBER}.
+Thus, at the $k$th stage, the bordering algorithm consists of
+solving the lower triangular system
+\begin{equation} \label{1.2}
+ L_{k-1}v = c
+\end{equation}
+and setting
+\begin{eqnarray}
+\ell &=& D^{-1}_{k-1}v , \\
+\delta &=& \alpha - \ell^{t} v .
+\end{eqnarray}
+
+\subsubsection{Versatility.} We do not
+attempt to present an overview
+here, but rather attempt to focus on those results that
+are relevant to our particular algorithm.
+
+\section{Conclusions} The special
+structure of this problem allows us to make exact estimates of
+the complexity. For the old approach, we show that the
+complexity of the intersection problem is $O(n^{3})$, the same
+as the complexity of the numerical computations
+\cite{GEORGELIU}, \cite{ROSEWHITTEN}. For the
+new approach, the complexity of the second part is reduced to
+$O(n^{2} (\log n)^{2})$.
+
+\begin{thebibliography}{99}
+
+
+\bibitem{BANKSMITH}
+R.~E. Bank and R.~K. Smith, {\em General sparse elimination requires no
+ permanent integer storage}, SIAM J. Sci. Stat. Comput., 8 (1987),
+ pp.~574--584.
+
+\bibitem{EISENSTAT}
+S.~C. Eisenstat, M.~C. Gursky, M.~Schultz, and A.~Sherman, {\em
+ Algorithms and data structures for sparse symmetric gaussian elimination},
+ SIAM J. Sci. Stat. Comput., 2 (1982), pp.~225--237.
+
+\bibitem{GEORGELIU}
+A.~George and J.~Liu, {\em Computer Solution of Large Sparse Positive
+ Definite Systems}, Prentice Hall, Englewood Cliffs, NJ, 1981.
+
+\bibitem{LAW}
+K.~H. Law and S.~J. Fenves, {\em A node addition model for symbolic
+ factorization}, ACM TOMS, 12 (1986), pp.~37--50.
+
+\bibitem{LIU}
+J.~W.~H. Liu, {\em A compact row storage scheme for cholesky factors
+ using elimination trees}, ACM TOMS, 12 (1986), pp.~127--148.
+
+\bibitem{LIU2}
+\sameauthor , {\em The role of
+ elimination trees in sparse factorization}, Tech. Report CS-87-12,Department
+ of Computer Science, York University, Ontario, Canada, 1987.
+
+\bibitem{ROSE72}
+D.~J. Rose, {\em A graph theoretic study of the numeric solution of
+ sparse positive definite systems}, in Graph Theory and Computing, Academic Press, New
+York, 1972.
+
+\bibitem{ROSE76}
+D.~J. Rose, R.~E. Tarjan, and G.~S. Lueker, {\em Algorithmic aspects of
+ vertex elimination on graphs}, SIAM J. Comput., 5 (1976), pp.~226--283.
+
+\bibitem{ROSEWHITTEN}
+D.~J. Rose and G.~F. Whitten, {\em A recursive analysis of disection
+ strategies}, in Sparse Matrix Computations, Academic Press, New York, 1976.
+
+\bibitem{SCHREIBER}
+R.~Schreiber, {\em A new implementation of sparse gaussian elimination},
+ ACM TOMS, 8 (1982), pp.~256--276.
+
+\end{thebibliography}
+
+\end{document}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% This is ltexproc.sty.
+% This file may be freely distributed but may not be altered in any way.
+% Any comments or questions regarding these macros should be directed to:
+
+% Corey Gray
+% SIAM
+% 3600 University City Science Center
+% Philadelphia, PA 19104-2688
+% USA
+% Telephone: (215) 382-9800
+% Fax: (215) 386-7999
+% e-mail: gray@siam.org
+
+% This is a file of macros and definitions for creating a chapter for
+% publication in the SIAM Proceedings series using LaTeX.
+
+% Report the version.
+\message{*** SIAM LaTeX Proceedings Series macro package, version 1.0,
+November 6, 1992 ***}
+
+\pretolerance=800
+\tolerance=10000
+\sloppy
+
+
+\vsize=56pc
+\hsize=36pc
+\baselineskip=13pt
+\hoffset -.5in
+\voffset -.5in
+\footskip=18pt
+\topmargin 24pt
+\headheight 12pt
+\headsep 15pt
+\textheight 53.5pc \advance\textheight by \topskip
+\textwidth 36pc
+\parskip 0pt
+\parindent 18pt
+\def\topfraction{.9}
+\def\textfraction{.1}
+\def\topnumber{2}
+%% footnotes to be set 8/10
+\def\footnotesize{\@setsize\footnotesize{11pt}\ixpt\@ixpt
+ % \indent
+ \abovedisplayskip \z@
+ \belowdisplayskip\z@
+ \abovedisplayshortskip\abovedisplayskip
+ \belowdisplayshortskip\belowdisplayshortskip
+\def\@listi{\leftmargin\leftmargini \topsep 3pt plus 1pt minus 1pt
+ \parsep 2pt plus 1pt minus 1pt
+ \itemsep \parsep}}
+
+\let\referencesize\footnotesize
+
+\footnotesep 0pt
+
+\skip\footins 12pt plus 12pt
+
+\def\footnoterule{\kern3\p@ \hrule width 3em\vspace{3pt}} % the \hrule is .4pt high
+
+
+\def\ps@plain{\let\@mkboth\@gobbletwo
+ \def\@oddfoot{{\hfil\small\thepage\hfil}}%
+ \def\@oddhead{}
+ \def\@evenhead{}\def\@evenfoot{}}
+
+
+
+\def\ps@headings{\let\@mkboth\markboth
+ \def\@oddfoot{}\def\@evenfoot{}%
+ \def\@evenhead{{\rm\thepage}\hspace*{2pc}{\sc\leftmark}\hfil}%
+ \def\@oddhead{\hfil{\noindent\sc\rightmark}\hspace*{2pc}{\rm\thepage}}%
+
+
+
+\def\ps@myheadings{\let\@mkboth\@gobbletwo
+ \def\@oddfoot{}\def\@evenfoot{}%
+ \def\@oddhead{\hfil{\sc\rightmark}\hspace*{2pc}{\normalsize\rm\thepage}}%
+ \def\@evenhead{{\normalsize\rm\thepage}\hspace*{2pc}{\sc\leftmark}\hfil}%
+% \def\chaptermark##1{}%
+ % \def\sectionmark##1{}\def\subsectionmark##1{}}
+}}
+
+
+
+\def\theequation{\arabic{equation}}
+
+\def\abstract{\if@twocolumn
+\section*{Abstract}
+\else \small
+\begin{center}
+{\bf Abstract\vspace{-.5em}\vspace{3pt}}
+\end{center}
+\quotation
+\fi}
+\def\endabstract{\if@twocolumn\else\endquotation\fi}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %
+% THEOREMS, PROOFS, ALGORITHMS %
+% %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%% defined proof environment by theorem model (took out counter)
+
+\def\qed{{\qquad \vbox{\hrule\hbox{%
+ \vrule height1.3ex\hskip0.8ex\vrule}\hrule
+ }}\par}
+
+\def\newproof#1{\@nprf{#1}}
+
+\def\@nprf#1#2{\@xnprf{#1}{#2}}
+
+\def\@xnprf#1#2{\expandafter\@ifdefinable\csname #1\endcsname
+\global\@namedef{#1}{\@prf{#1}{#2}}\global\@namedef{end#1}{\@endproof}}
+
+\def\@prf#1#2{\@xprf{#1}{#2}}
+
+\def\@xprf#1#2{\@beginproof{#2}{\csname the#1\endcsname}\ignorespaces}
+
+
+
+%%% defined algorithm environment by theorem model
+
+\def\newalgorithm#1{\@ifnextchar[{\@oalg{#1}}{\@nalg{#1}}}
+
+\def\@nalg#1#2{%
+\@ifnextchar[{\@xnalg{#1}{#2}}{\@ynalg{#1}{#2}}}
+
+\def\@xnalg#1#2[#3]{\expandafter\@ifdefinable\csname #1\endcsname
+{\@definecounter{#1}\@addtoreset{#1}{#3}%
+\expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand
+ \csname the#3\endcsname \@thmcountersep \@thmcounter{#1}}%
+\global\@namedef{#1}{\@alg{#1}{#2}}\global\@namedef{end#1}{\@endalgorithm}}}
+
+\def\@ynalg#1#2{\expandafter\@ifdefinable\csname #1\endcsname
+{\@definecounter{#1}%
+\expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}%
+\global\@namedef{#1}{\@alg{#1}{#2}}\global\@namedef{end#1}{\@endalgorithm}}}
+
+\def\@oalg#1[#2]#3{\expandafter\@ifdefinable\csname #1\endcsname
+ {\global\@namedef{the#1}{\@nameuse{the#2}}%
+\global\@namedef{#1}{\@alg{#2}{#3}}%
+\global\@namedef{end#1}{\@endalgorithm}}}
+
+\def\@alg#1#2{\refstepcounter
+ {#1}\@ifnextchar[{\@yalg{#1}{#2}}{\@xalg{#1}{#2}}}
+
+\def\@xalg#1#2{\@beginalgorithm{#2}{\csname the#1\endcsname}\ignorespaces}
+\def\@yalg#1#2[#3]{\@opargbeginalgorithm{#2}{\csname
+ the#1\endcsname}{#3}\ignorespaces}
+
+
+
+
+\def\@beginproof#1{\rm {\it #1.\ }}
+\def\@endproof{\outerparskip 0pt\endtrivlist}
+
+\def\@begintheorem#1#2{\it {\sc #1\ #2.\ }}
+\def\@opargbegintheorem#1#2#3{\it
+ {\sc #1\ #2\ (#3).\ }}
+\def\@endtheorem{\outerparskip 0pt\endtrivlist}
+
+%\def\@begindefinition#1#2{\rm \trivlist \item[\hskip \labelsep{\sc #1\ #2.}]}
+%\def\@opargbegindefinition#1#2#3{\rm \trivlist
+% \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]}
+%\def\@enddefinition{\outerparskip 0pt\endtrivlist}
+
+
+\def\@beginalgorithm#1#2{\rm \trivlist \item[\hskip \labelsep{\sc #1\ #2.}]}
+\def\@opargbeginalgorithm#1#2#3{\rm \trivlist
+ \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]}
+\def\@endalgorithm{\outerparskip 6pt\endtrivlist}
+
+
+\newskip\outerparskip
+
+\def\trivlist{\parsep\outerparskip
+ \@trivlist \labelwidth\z@ \leftmargin\z@
+ \itemindent\parindent \def\makelabel##1{##1}}
+
+\def\@trivlist{\topsep=0pt\@topsepadd\topsep
+ \if@noskipsec \leavevmode \fi
+ \ifvmode \advance\@topsepadd\partopsep \else \unskip\par\fi
+ \if@inlabel \@noparitemtrue \@noparlisttrue
+ \else \@noparlistfalse \@topsep\@topsepadd \fi
+ \advance\@topsep \parskip
+ \leftskip\z@\rightskip\@rightskip \parfillskip\@flushglue
+ \@setpar{\if@newlist\else{\@@par}\fi}%
+ \global\@newlisttrue \@outerparskip\parskip}
+
+
+\def\endtrivlist{\if@newlist\@noitemerr\fi
+ \if@inlabel\indent\fi
+ \ifhmode\unskip \par\fi
+ \if@noparlist \else
+ \ifdim\lastskip >\z@ \@tempskipa\lastskip \vskip -\lastskip
+ \advance\@tempskipa\parskip \advance\@tempskipa -\@outerparskip
+ \vskip\@tempskipa
+ \fi\@endparenv\fi
+ \vskip\outerparskip}
+
+
+
+ \newproof{@proof}{Proof}
+ \newenvironment{proof}{\begin{@proof}}{\end{@proof}}
+
+ \newtheorem{@theorem}{Theorem}[section]
+ \newenvironment{theorem}{\begin{@theorem}}{\end{@theorem}}
+
+% \newalgorithm{@algorithm}{Algorithm}[section]
+% \newenvironment{algorithm}{\begin{@algorithm}}{\end{@algorithm}}
+
+
+
+\newtheorem{lemma}{Lemma}[section]
+\newtheorem{fact}{Fact}[section]
+\newtheorem{corollary}{Corollary}[section]
+\newtheorem{axiom}{Axiom}[section]
+\newtheorem{cond}{Condition}[section]
+\newtheorem{property}{Property}[section]
+\newtheorem{proposition}{Proposition}[section]
+
+\newtheorem{Conjecture}{Conjecture}[section]
+\newtheorem{Definition}{Definition}[section]
+\newtheorem{Lemma}{Lemma}[section]
+\newtheorem{Remark}{Remark}[section]
+
+\newproof{Example}{Example}
+\newproof{Method}{Method}
+\newproof{Exercise}{Exercise}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %
+% TABLE AND FIGURE CAPTIONS %
+% %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \def\@figtxt{figure}
+\long\def\@makecaption#1#2{\small
+\setlength{\parindent}{18pt}
+\baselineskip 14pt
+ \ifx\@captype\@figtxt
+ \vskip 10pt
+ \setbox\@tempboxa\hbox{{\sc #1} {\it #2}}
+ \ifdim \wd\@tempboxa >\hsize {\sc #1} {\it #2}\par \else \hbox
+to\hsize{\hfil\box\@tempboxa\hfil}%
+ \fi\else\hbox to\hsize{\hfil{\sc #1}\hfil}%
+ \setbox\@tempboxa\hbox{{\it #2}}%
+ \ifdim \wd\@tempboxa >\hsize {\it #2}\par \else
+ \hbox to \hsize{\hfil\box\@tempboxa\hfil}\fi
+ \vskip 10pt
+ \fi}
+
+
+%\newif\iftable \global\tablefalse
+
+
+%\long\def\@makecaption#1#2{%
+%\setlength{\parindent}{18pt}
+% \vskip 12pt
+% \iftable
+ % \hbox to \hsize{\hfil\sc #1\hfil}
+ % \hbox to \hsize{\hfil\it #2\hfil}
+ % \global\tablefalse
+ % \else
+ % \setbox\@tempboxa\hbox{{\small#1} {\small\it#2}}
+ % \ifdim \wd\@tempboxa >\hsize
+ % \indent{\small#1}{\small\it#2}\par
+ % \else
+ % \hbox to\hsize{\hfil\box\@tempboxa\hfil}\fi
+ % \fi}
+% \vskip 6pt}
+
+
+
+%\def\figure{\global\tablefalse\@float{figure}}
+\def\fnum@figure{\par\sc Fig. \thefigure.\ }
+%\def\fnum@figure{\par\sc Fig. \thefigure\ }
+
+%\def\table{\global\tabletrue\@float{table}}
+\def\fnum@table{\small \sc Table \thetable}
+
+
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %
+% SECTIONS %
+% %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\def\section{\@startsection {section}{1}{\z@}{-3.5ex plus -1ex minus
+ -.2ex}%{2.3ex plus .2ex}
+{2pt}{\large\bf}}
+\def\subsection{\@startsection{subsection}{2}{\z@}{-3.25ex plus -1ex minus
+ -.2ex}%{1.5ex plus .2ex}
+{2pt}{\large\bf}}
+\def\subsubsection{\@startsection {subsubsection}{3}{\z@}{1.3ex plus .5ex minus
+ .2ex}{-.5em plus -.1em}{\normalsize\bf}}
+
+
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% %%
+%% BIBLIOGRAPHY %%
+%% %%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+\def\thebibliography#1{%
+%\cleardoublepage
+\parindent 0em
+\vspace{9pt}
+\begin{flushleft}\large\bf {References}\end{flushleft}
+\addvspace{3pt}\nopagebreak\list
+ %% default is no labels, for those not using \cite or BibTeX
+{[\arabic{enumi}]} {\settowidth\labelwidth{[#1]}
+%%{[\arabic{enumi}]}{\settowidth\labelwidth{mm}
+\leftmargin\labelwidth
+\leftmargin=17pt
+ \advance\leftmargin\labelsep
+ \usecounter{enumi}\@bibsetup}
+\def\newblock{\hskip .11em plus .33em minus -.07em}
+ \sloppy\clubpenalty4000\widowpenalty4000
+ \sfcode`\.=1000\relax}
+
+
+
+%% setup 8/10 type
+\def\@bibsetup{%\itemindent=0pt
+\itemsep=0pt \parsep=0pt
+\small}
+
+\def\sameauthor{\leavevmode\vrule height 2pt depth -1.6pt width 23pt}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %
+% INDEX %
+% %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%makeindex.sty official version 6.4
+%The second line came from /usr/misc/lib/tex82/report.sty.
+
+\def\theindex{\@restonecoltrue\if@twocolumn\@restonecolfalse\fi
+\columnseprule \z@
+\columnsep 35pt\twocolumn[\chapter*{Index}]
+ \parskip\z@ plus .3pt\relax\let\item\@idxitem}
+
+
+\def\printindex{\cleardoublepage\markboth{INDEX}{INDEX}
+\addcontentsline{toc}{chapter}{Index}\@input{\jobname.ind}}
+
+\ps@headings
+
+
+%%% end of style file
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% This is siamproc.bst
+% SIAM bibliography style (29-Jan-88 version)
+% numeric labels, alphabetic order, Mathematical Reviews abbreviations,
+% names in \sc, titles in italics, book titles mixed upper-lower and article
+% titles lowercase, commas separate all fields except before "notes".
+%
+% History
+% 1/30/86 (HWT) Original version, by Howard Trickey.
+% 6/15/87 (HWT) Fix format.editors---Martin Costabel.
+% 1/29/88 (OP&HWT) Updated for BibTeX version 0.99a, Oren Patashnik;
+% THIS `siam' VERSION DOES NOT WORK WITH BIBTEX 0.98i.
+
+ENTRY
+ { address
+ author
+ booktitle
+ chapter
+ edition
+ editor
+ howpublished
+ institution
+ journal
+ key
+ month
+ note
+ number
+ organization
+ pages
+ publisher
+ school
+ series
+ title
+ type
+ volume
+ year
+ }
+ {}
+ { label }
+
+INTEGERS { output.state before.all mid.sentence after.block }
+
+FUNCTION {init.state.consts}
+{ #0 'before.all :=
+ #1 'mid.sentence :=
+ #2 'after.block :=
+}
+
+STRINGS { s t }
+
+FUNCTION {output.nonnull}
+{ 's :=
+ output.state mid.sentence =
+ { ", " * write$ }
+ { output.state after.block =
+ { add.period$ write$
+ newline$
+ "\newblock " write$
+ }
+ 'write$
+ if$
+ mid.sentence 'output.state :=
+ }
+ if$
+ s
+}
+
+FUNCTION {output}
+{ duplicate$ empty$
+ 'pop$
+ 'output.nonnull
+ if$
+}
+
+FUNCTION {output.check}
+{ 't :=
+ duplicate$ empty$
+ { pop$ "empty " t * " in " * cite$ * warning$ }
+ 'output.nonnull
+ if$
+}
+
+FUNCTION {output.bibitem}
+{ newline$
+ "\bibitem{" write$
+ cite$ write$
+ "}" write$
+ newline$
+ ""
+ before.all 'output.state :=
+}
+
+FUNCTION {fin.entry}
+{ add.period$
+ write$
+ newline$
+}
+
+FUNCTION {new.block}
+{ output.state before.all =
+ 'skip$
+ { after.block 'output.state := }
+ if$
+}
+
+FUNCTION {not}
+{ { #0 }
+ { #1 }
+ if$
+}
+
+FUNCTION {and}
+{ 'skip$
+ { pop$ #0 }
+ if$
+}
+
+FUNCTION {or}
+{ { pop$ #1 }
+ 'skip$
+ if$
+}
+
+FUNCTION {new.block.checka}
+{ empty$
+ 'skip$
+ 'new.block
+ if$
+}
+
+FUNCTION {field.or.null}
+{ duplicate$ empty$
+ { pop$ "" }
+ 'skip$
+ if$
+}
+
+FUNCTION {emphasize}
+{ duplicate$ empty$
+ { pop$ "" }
+ { "{\em " swap$ * "}" * }
+ if$
+}
+
+FUNCTION {scapify}
+{ duplicate$ empty$
+ { pop$ "" }
+ { "{\sc " swap$ * "}" * }
+ if$
+}
+
+INTEGERS { nameptr namesleft numnames }
+
+FUNCTION {format.names}
+{ 's :=
+ #1 'nameptr :=
+ s num.names$ 'numnames :=
+ numnames 'namesleft :=
+ { namesleft #0 > }
+ { s nameptr "{f.~}{vv~}{ll}{, jj}" format.name$ 't :=
+ nameptr #1 >
+ { namesleft #1 >
+ { ", " * t * }
+ { numnames #2 >
+ { "," * }
+ 'skip$
+ if$
+ t "others" =
+ { " et~al." * }
+ { " and " * t * }
+ if$
+ }
+ if$
+ }
+ 't
+ if$
+ nameptr #1 + 'nameptr :=
+ namesleft #1 - 'namesleft :=
+ }
+ while$
+}
+
+STRINGS { last.authors }
+
+FUNCTION {init.last.authors}
+{ "" 'last.authors :=
+}
+
+FUNCTION {format.authors}
+{ author empty$
+ { "" 'last.authors :=
+ ""
+ }
+ { author last.authors =
+ { "\leavevmode\vrule height 2pt depth -1.6pt width 23pt" }
+ { author format.names }% scapify }
+ if$
+ author 'last.authors :=
+ }
+ if$
+}
+
+FUNCTION {format.organization}
+{ organization empty$
+ { "" 'last.authors :=
+ ""
+ }
+ { organization last.authors =
+ { "\leavevmode\vrule height 2pt depth -1.6pt width 23pt" }
+ { organization scapify }
+ if$
+ organization 'last.authors :=
+ }
+ if$
+}
+
+FUNCTION {format.editors}
+{ editor empty$
+ { "" 'last.authors :=
+ ""
+ }
+ { editor last.authors =
+ { "\leavevmode\vrule height 2pt depth -1.6pt width 23pt" }
+ { editor format.names scapify }
+ if$
+ editor num.names$ #1 >
+ { ", eds." * }
+ { ", ed." * }
+ if$
+ editor 'last.authors :=
+ }
+ if$
+}
+
+FUNCTION {format.ineditors}
+{ editor empty$
+ { "" }
+ { editor format.names
+ editor num.names$ #1 >
+ { ", eds." * }
+ { ", ed." * }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.title}
+{ title empty$
+ { "" }
+ { title "t" change.case$ emphasize }
+ if$
+}
+
+FUNCTION {n.dashify}
+{ 't :=
+ ""
+ { t empty$ not }
+ { t #1 #1 substring$ "-" =
+ { t #1 #2 substring$ "--" = not
+ { "--" *
+ t #2 global.max$ substring$ 't :=
+ }
+ { { t #1 #1 substring$ "-" = }
+ { "-" *
+ t #2 global.max$ substring$ 't :=
+ }
+ while$
+ }
+ if$
+ }
+ { t #1 #1 substring$ *
+ t #2 global.max$ substring$ 't :=
+ }
+ if$
+ }
+ while$
+}
+
+FUNCTION {format.date}
+{ year empty$
+ { month empty$
+ { "" }
+ { "there's a month but no year in " cite$ * warning$
+ month
+ }
+ if$
+ }
+ { month empty$
+ 'year
+ { month " " * year * }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.btitle}
+{ title emphasize
+}
+
+FUNCTION {tie.or.space.connect}
+{ duplicate$ text.length$ #3 <
+ { "~" }
+ { " " }
+ if$
+ swap$ * *
+}
+
+FUNCTION {either.or.check}
+{ empty$
+ 'pop$
+ { "can't use both " swap$ * " fields in " * cite$ * warning$ }
+ if$
+}
+
+FUNCTION {format.bvolume}
+{ volume empty$
+ { "" }
+ { "vol.~" volume *
+ series empty$
+ 'skip$
+ { " of " * series * }
+ if$
+ "volume and number" number either.or.check
+ }
+ if$
+}
+
+FUNCTION {format.number.series}
+{ volume empty$
+ { number empty$
+ { series field.or.null }
+ { "no.~" number *
+ series empty$
+ { "there's a number but no series in " cite$ * warning$ }
+ { " in " * series * }
+ if$
+ }
+ if$
+ }
+ { "" }
+ if$
+}
+
+FUNCTION {format.edition}
+{ edition empty$
+ { "" }
+ { edition "l" change.case$ "~ed." * }
+ if$
+}
+
+INTEGERS { multiresult }
+
+FUNCTION {multi.page.check}
+{ 't :=
+ #0 'multiresult :=
+ { multiresult not
+ t empty$ not
+ and
+ }
+ { t #1 #1 substring$
+ duplicate$ "-" =
+ swap$ duplicate$ "," =
+ swap$ "+" =
+ or or
+ { #1 'multiresult := }
+ { t #2 global.max$ substring$ 't := }
+ if$
+ }
+ while$
+ multiresult
+}
+
+FUNCTION {format.pages}
+{ pages empty$
+ { "" }
+ { pages multi.page.check
+ { "pp.~" pages n.dashify * }
+ { "p.~" pages * }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.vol.year}
+{ volume field.or.null
+ year empty$
+ { "empty year in " cite$ * warning$ }
+ { " (" year * ")" * * }
+ if$
+}
+
+FUNCTION {format.chapter.pages}
+{ chapter empty$
+ 'format.pages
+ { type empty$
+ { "ch.~" chapter * }
+ { type "l" change.case$ chapter tie.or.space.connect }
+ if$
+ pages empty$
+ 'skip$
+ { ", " * format.pages * }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.in.ed.booktitle}
+{ booktitle empty$
+ { "" }
+ { editor empty$
+ { "in " booktitle * }
+ { "in " booktitle * ", " * format.ineditors * }
+ if$
+ }
+ if$
+}
+
+FUNCTION {empty.misc.check}
+{ author empty$ title empty$ howpublished empty$
+ month empty$ year empty$ note empty$
+ and and and and and
+ key empty$ not and
+ { "all relevant fields are empty in " cite$ * warning$ }
+ 'skip$
+ if$
+}
+
+FUNCTION {format.thesis.type}
+{ type empty$
+ 'skip$
+ { pop$
+ type "l" change.case$
+ }
+ if$
+}
+
+FUNCTION {format.tr.number}
+{ type empty$
+ { "Tech. Rep." }
+ 'type
+ if$
+ number empty$
+ { "l" change.case$ }
+ { number tie.or.space.connect }
+ if$
+}
+
+FUNCTION {format.article.crossref}
+{ key empty$
+ { journal empty$
+ { "need key or journal for " cite$ * " to crossref " * crossref *
+ warning$
+ ""
+ }
+ { "in " journal * }
+ if$
+ }
+ { "in " key * }
+ if$
+ " \cite{" * crossref * "}" *
+}
+
+FUNCTION {format.crossref.editor}
+{ editor #1 "{vv~}{ll}" format.name$
+ editor num.names$ duplicate$
+ #2 >
+ { pop$ " et~al." * }
+ { #2 <
+ 'skip$
+ { editor #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" =
+ { " et~al." * }
+ { " and " * editor #2 "{vv~}{ll}" format.name$ * }
+ if$
+ }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.book.crossref}
+{ volume empty$
+ { "empty volume in " cite$ * "'s crossref of " * crossref * warning$
+ "in "
+ }
+ { "vol.~" volume *
+ " of " *
+ }
+ if$
+ editor empty$
+ editor field.or.null author field.or.null =
+ or
+ { key empty$
+ { series empty$
+ { "need editor, key, or series for " cite$ * " to crossref " *
+ crossref * warning$
+ "" *
+ }
+ { series * }
+ if$
+ }
+ { key * }
+ if$
+ }
+ { format.crossref.editor * }
+ if$
+ " \cite{" * crossref * "}" *
+}
+
+FUNCTION {format.incoll.inproc.crossref}
+{ editor empty$
+ editor field.or.null author field.or.null =
+ or
+ { key empty$
+ { booktitle empty$
+ { "need editor, key, or booktitle for " cite$ * " to crossref " *
+ crossref * warning$
+ ""
+ }
+ { "in " booktitle * }
+ if$
+ }
+ { "in " key * }
+ if$
+ }
+ { "in " format.crossref.editor * }
+ if$
+ " \cite{" * crossref * "}" *
+}
+
+FUNCTION {article}
+{ output.bibitem
+ format.authors "author" output.check
+ format.title "title" output.check
+ crossref missing$
+ { journal "journal" output.check
+ format.vol.year output
+ }
+ { format.article.crossref output.nonnull }
+ if$
+ format.pages output
+ new.block
+ note output
+ fin.entry
+}
+
+FUNCTION {book}
+{ output.bibitem
+ author empty$
+ { format.editors "author and editor" output.check }
+ { format.authors output.nonnull
+ crossref missing$
+ { "author and editor" editor either.or.check }
+ 'skip$
+ if$
+ }
+ if$
+ format.btitle "title" output.check
+ crossref missing$
+ { format.bvolume output
+ format.number.series output
+ publisher "publisher" output.check
+ address output
+ }
+ { format.book.crossref output.nonnull }
+ if$
+ format.edition output
+ format.date "year" output.check
+ new.block
+ note output
+ fin.entry
+}
+
+FUNCTION {booklet}
+{ output.bibitem
+ format.authors output
+ format.title "title" output.check
+ howpublished new.block.checka
+ howpublished output
+ address output
+ format.date output
+ new.block
+ note output
+ fin.entry
+}
+
+FUNCTION {inbook}
+{ output.bibitem
+ author empty$
+ { format.editors "author and editor" output.check }
+ { format.authors output.nonnull
+ crossref missing$
+ { "author and editor" editor either.or.check }
+ 'skip$
+ if$
+ }
+ if$
+ format.btitle "title" output.check
+ crossref missing$
+ { format.bvolume output
+ format.number.series output
+ publisher "publisher" output.check
+ address output
+ }
+ { format.book.crossref output.nonnull }
+ if$
+ format.edition output
+ format.date "year" output.check
+ format.chapter.pages "chapter and pages" output.check
+ new.block
+ note output
+ fin.entry
+}
+
+FUNCTION {incollection}
+{ output.bibitem
+ format.authors "author" output.check
+ format.title "title" output.check
+ crossref missing$
+ { format.in.ed.booktitle "booktitle" output.check
+ format.bvolume output
+ format.number.series output
+ publisher "publisher" output.check
+ address output
+ format.edition output
+ format.date "year" output.check
+ }
+ { format.incoll.inproc.crossref output.nonnull }
+ if$
+ format.chapter.pages output
+ new.block
+ note output
+ fin.entry
+}
+
+FUNCTION {inproceedings}
+{ output.bibitem
+ format.authors "author" output.check
+ format.title "title" output.check
+ crossref missing$
+ { format.in.ed.booktitle "booktitle" output.check
+ format.bvolume output
+ format.number.series output
+ address empty$
+ { organization output
+ publisher output
+ format.date "year" output.check
+ }
+ { address output.nonnull
+ format.date "year" output.check
+ organization output
+ publisher output
+ }
+ if$
+ }
+ { format.incoll.inproc.crossref output.nonnull }
+ if$
+ format.pages output
+ new.block
+ note output
+ fin.entry
+}
+
+FUNCTION {conference} { inproceedings }
+
+FUNCTION {manual}
+{ output.bibitem
+ author empty$
+ { format.organization output }
+ { format.authors output.nonnull }
+ if$
+ format.btitle "title" output.check
+ author empty$
+ 'skip$
+ { organization output }
+ if$
+ address output
+ format.edition output
+ format.date output
+ new.block
+ note output
+ fin.entry
+}
+
+FUNCTION {mastersthesis}
+{ output.bibitem
+ format.authors "author" output.check
+ format.title "title" output.check
+ "Master's thesis" format.thesis.type output.nonnull
+ school "school" output.check
+ address output
+ format.date "year" output.check
+ new.block
+ note output
+ fin.entry
+}
+
+FUNCTION {misc}
+{ output.bibitem
+ format.authors output
+ format.title output
+ howpublished new.block.checka
+ howpublished output
+ format.date output
+ new.block
+ note output
+ fin.entry
+ empty.misc.check
+}
+
+FUNCTION {phdthesis}
+{ output.bibitem
+ format.authors "author" output.check
+ format.btitle "title" output.check
+ "PhD thesis" format.thesis.type output.nonnull
+ school "school" output.check
+ address output
+ format.date "year" output.check
+ new.block
+ note output
+ fin.entry
+}
+
+FUNCTION {proceedings}
+{ output.bibitem
+ editor empty$
+ { format.organization output }
+ { format.editors output.nonnull }
+ if$
+ format.btitle "title" output.check
+ format.bvolume output
+ format.number.series output
+ address empty$
+ { editor empty$
+ 'skip$
+ { organization output }
+ if$
+ publisher output
+ format.date "year" output.check
+ }
+ { address output.nonnull
+ format.date "year" output.check
+ editor empty$
+ 'skip$
+ { organization output }
+ if$
+ publisher output
+ }
+ if$
+ new.block
+ note output
+ fin.entry
+}
+
+FUNCTION {techreport}
+{ output.bibitem
+ format.authors "author" output.check
+ format.title "title" output.check
+ format.tr.number output.nonnull
+ institution "institution" output.check
+ address output
+ format.date "year" output.check
+ new.block
+ note output
+ fin.entry
+}
+
+FUNCTION {unpublished}
+{ output.bibitem
+ format.authors "author" output.check
+ format.title "title" output.check
+ new.block
+ note "note" output.check
+ format.date output
+ fin.entry
+}
+
+FUNCTION {default.type} { misc }
+
+MACRO {jan} {"Jan."}
+
+MACRO {feb} {"Feb."}
+
+MACRO {mar} {"Mar."}
+
+MACRO {apr} {"Apr."}
+
+MACRO {may} {"May"}
+
+MACRO {jun} {"June"}
+
+MACRO {jul} {"July"}
+
+MACRO {aug} {"Aug."}
+
+MACRO {sep} {"Sept."}
+
+MACRO {oct} {"Oct."}
+
+MACRO {nov} {"Nov."}
+
+MACRO {dec} {"Dec."}
+
+MACRO {acmcs} {"ACM Comput. Surveys"}
+
+MACRO {acta} {"Acta Inf."}
+
+MACRO {cacm} {"Comm. ACM"}
+
+MACRO {ibmjrd} {"IBM J. Res. Dev."}
+
+MACRO {ibmsj} {"IBM Syst.~J."}
+
+MACRO {ieeese} {"IEEE Trans. Softw. Eng."}
+
+MACRO {ieeetc} {"IEEE Trans. Comput."}
+
+MACRO {ieeetcad}
+ {"IEEE Trans. Comput.-Aided Design Integrated Circuits"}
+
+MACRO {ipl} {"Inf. Process. Lett."}
+
+MACRO {jacm} {"J.~Assoc. Comput. Mach."}
+
+MACRO {jcss} {"J.~Comput. System Sci."}
+
+MACRO {scp} {"Sci. Comput. Programming"}
+
+MACRO {sicomp} {"SIAM J. Comput."}
+
+MACRO {tocs} {"ACM Trans. Comput. Syst."}
+
+MACRO {tods} {"ACM Trans. Database Syst."}
+
+MACRO {tog} {"ACM Trans. Gr."}
+
+MACRO {toms} {"ACM Trans. Math. Softw."}
+
+MACRO {toois} {"ACM Trans. Office Inf. Syst."}
+
+MACRO {toplas} {"ACM Trans. Prog. Lang. Syst."}
+
+MACRO {tcs} {"Theoretical Comput. Sci."}
+
+READ
+
+FUNCTION {sortify}
+{ purify$
+ "l" change.case$
+}
+
+INTEGERS { len }
+
+FUNCTION {chop.word}
+{ 's :=
+ 'len :=
+ s #1 len substring$ =
+ { s len #1 + global.max$ substring$ }
+ 's
+ if$
+}
+
+FUNCTION {sort.format.names}
+{ 's :=
+ #1 'nameptr :=
+ ""
+ s num.names$ 'numnames :=
+ numnames 'namesleft :=
+ { namesleft #0 > }
+ { nameptr #1 >
+ { " " * }
+ 'skip$
+ if$
+ s nameptr "{vv{ } }{ll{ }}{ f{ }}{ jj{ }}" format.name$ 't :=
+ nameptr numnames = t "others" = and
+ { "et al" * }
+ { t sortify * }
+ if$
+ nameptr #1 + 'nameptr :=
+ namesleft #1 - 'namesleft :=
+ }
+ while$
+}
+
+FUNCTION {sort.format.title}
+{ 't :=
+ "A " #2
+ "An " #3
+ "The " #4 t chop.word
+ chop.word
+ chop.word
+ sortify
+ #1 global.max$ substring$
+}
+
+FUNCTION {author.sort}
+{ author empty$
+ { key empty$
+ { "to sort, need author or key in " cite$ * warning$
+ ""
+ }
+ { key sortify }
+ if$
+ }
+ { author sort.format.names }
+ if$
+}
+
+FUNCTION {author.editor.sort}
+{ author empty$
+ { editor empty$
+ { key empty$
+ { "to sort, need author, editor, or key in " cite$ * warning$
+ ""
+ }
+ { key sortify }
+ if$
+ }
+ { editor sort.format.names }
+ if$
+ }
+ { author sort.format.names }
+ if$
+}
+
+FUNCTION {author.organization.sort}
+{ author empty$
+ { organization empty$
+ { key empty$
+ { "to sort, need author, organization, or key in " cite$ * warning$
+ ""
+ }
+ { key sortify }
+ if$
+ }
+ { "The " #4 organization chop.word sortify }
+ if$
+ }
+ { author sort.format.names }
+ if$
+}
+
+FUNCTION {editor.organization.sort}
+{ editor empty$
+ { organization empty$
+ { key empty$
+ { "to sort, need editor, organization, or key in " cite$ * warning$
+ ""
+ }
+ { key sortify }
+ if$
+ }
+ { "The " #4 organization chop.word sortify }
+ if$
+ }
+ { editor sort.format.names }
+ if$
+}
+
+FUNCTION {presort}
+{ type$ "book" =
+ type$ "inbook" =
+ or
+ 'author.editor.sort
+ { type$ "proceedings" =
+ 'editor.organization.sort
+ { type$ "manual" =
+ 'author.organization.sort
+ 'author.sort
+ if$
+ }
+ if$
+ }
+ if$
+ " "
+ *
+ year field.or.null sortify
+ *
+ " "
+ *
+ title field.or.null
+ sort.format.title
+ *
+ #1 entry.max$ substring$
+ 'sort.key$ :=
+}
+
+ITERATE {presort}
+
+SORT
+
+STRINGS { longest.label }
+
+INTEGERS { number.label longest.label.width }
+
+FUNCTION {initialize.longest.label}
+{ "" 'longest.label :=
+ #1 'number.label :=
+ #0 'longest.label.width :=
+}
+
+FUNCTION {longest.label.pass}
+{ number.label int.to.str$ 'label :=
+ number.label #1 + 'number.label :=
+ label width$ longest.label.width >
+ { label 'longest.label :=
+ label width$ 'longest.label.width :=
+ }
+ 'skip$
+ if$
+}
+
+EXECUTE {initialize.longest.label}
+
+ITERATE {longest.label.pass}
+
+FUNCTION {begin.bib}
+{ preamble$ empty$
+ 'skip$
+ { preamble$ write$ newline$ }
+ if$
+ "\begin{thebibliography}{" longest.label * "}" * write$ newline$
+}
+
+EXECUTE {begin.bib}
+
+EXECUTE {init.state.consts}
+
+EXECUTE {init.last.authors}
+
+ITERATE {call.type$}
+
+FUNCTION {end.bib}
+{ newline$
+ "\end{thebibliography}" write$ newline$
+}
+
+EXECUTE {end.bib}
+