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{\Large Department of Mathematics, BGU}

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{\Huge Combinatorics Seminar}\\[0.2\baselineskip]

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\textbf{On} \emph{Tuesday, December  4, 2018}
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\textbf{At} \emph{15:30 -- 17:00}
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\textbf{In} \emph{201}

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{\large\scshape Arnold Filtser 
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  (BGU)
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will talk about
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{\Large\bfseries Steiner Point Removal with distortion O(log k), using the Relaxed Voronoi algorithm\par}
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\textsc{Abstract:}
In the Steiner Point Removal (SPR) problem, we are given a weighted graph \$G=(V,E)\$ and a set of terminals \$K\textbackslash{}subset V\$ of size \$k\$.
The objective is to find a minor \$M\$ of \$G\$ with only the terminals as its vertex set, such that distances between the terminals will be preserved up to a small multiplicative distortion.
Kamma, Krauthgamer and Nguyen {[}SICOMP2015{]} devised a ball-growing algorithm with exponential distributions to show that the distortion is at most \$O(\textbackslash{}log\^{}5 k)\$.
Cheung {[}SODA2018{]} improved the analysis of the same algorithm, bounding the distortion by \$O(\textbackslash{}log\^{}2 k)\$.
We devise a novel and simpler algorithm (called the Relaxed Voronoi algorithm) which incurs distortion \$O(\textbackslash{}log k)\$. This algorithm can be implemented in almost linear time (\$O(\textbar{}E\textbar{}\textbackslash{}log \textbar{}V\textbar{})\$).





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{\bfseries Please Note the Unusual Time and Place!}
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