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author | Karl Berry <karl@freefriends.org> | 2019-07-16 21:15:59 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2019-07-16 21:15:59 +0000 |
commit | 40e72a1b3cd2754403a94a15dc7ffc447d966ac8 (patch) | |
tree | b4f52b9b51370e56d0d65a34542f07269caafe9e /Master/texmf-dist/doc/xelatex/yazd-thesis/eninfo.tex | |
parent | e60e39769f3e2422fce8df70f0475a8d77c83000 (diff) |
yazd-thesis (16jul19)
git-svn-id: svn://tug.org/texlive/trunk@51655 c570f23f-e606-0410-a88d-b1316a301751
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diff --git a/Master/texmf-dist/doc/xelatex/yazd-thesis/eninfo.tex b/Master/texmf-dist/doc/xelatex/yazd-thesis/eninfo.tex new file mode 100644 index 00000000000..4a8325ffbc9 --- /dev/null +++ b/Master/texmf-dist/doc/xelatex/yazd-thesis/eninfo.tex @@ -0,0 +1,37 @@ +% در این فایل، عنوان پایاننامه، مشخصات خود و چکیده پایاننامه را به انگلیسی وارد کنید. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{latin} +\latincampus{Sciences Campus} +\latinfaculty{Faculty of Sciences} +\latindepartment{Department of Mathematical Sciences} +\latinfield{Communications (System)} +\latintitle{English Title of the Thesis} +\firstlatinsupervisor{First Supervisor} +\secondlatinsupervisor{Second Supervisor} +\firstlatinadvisor{First Advisor} +\secondlatinadvisor{Second Advisor} +\latinname{Nasser} +\latinsurname{Dehghan} +\latinthesisdate{January 2015} + +\enabstract{ +\subsection*{Abstract} +\thispagestyle{empty} +\baselineskip=1cm + +In this thesis, we study $1 + \varepsilon$-spanners for a set of $n$ points in the plane and in + d-dimensional Euclidean space that can be maintained efficiently as the points move. The + kinetic spanner in the plane has size $O(n/\varepsilon^{2})$. Assuming the trajectories of +the points can be described by polynomials whose degrees are at most $s$, +the number of events is $O(n^{2}\beta(n))$ ($\beta(n)$ grows slower than logarithmic functions), + and at each event the spanner can be updated in $O(1)$ time. The kinetic spanner in $\mathbb{R}^{d}$ has + size $O(n/\varepsilon^{d-1})$ and maximum degree $O(\log^{d} n)$. Assuming that the +trajectories of the points can be described by bounded-degree polynomials, the number of + events is $O(n^{2}/\varepsilon^{d-1})$, and using a supporting data +structure of size $O((n/\varepsilon^{d-1})\log^{d} n)$, we can handle events in + time $O(\log^{d+1} n)$. Moreover, the spanner can be updated in time $O(\log n/\varepsilon^{d-1})$ if + the flight plan of a point changes. These spanners are the first kinetic spanners whose performance does not depend on +the spread of the point set. +} +\latinyazdtitle +\end{latin} |