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- W2157665775 abstract "Given a set $mathsf{P}$ of $n$ points in $mathbb{R}^d$, we show how to insert a set $mathsf{X}$ of $O( n^{1-1/d} )$ additional points, such that $mathsf{P}$ can be broken into two sets $mathsf{P}_1$ and $mathsf{P}_2$, of roughly equal size, such that in the Voronoi diagram $mathcal{V}( mathsf{P} cup mathsf{X} )$, the cells of $mathsf{P}_1$ do not touch the cells of $mathsf{P}_2$; that is, $mathsf{X}$ separates $mathsf{P}_1$ from $mathsf{P}_2$ in the Voronoi diagram. Given such a partition $(mathsf{P}_1,mathsf{P}_2)$ of $mathsf{P}$, we present approximation algorithms to compute the minimum size separator realizing this partition. Finally, we present a simple local search algorithm that is a PTAS for geometric hitting set of fat objects (which can also be used to approximate the optimal Voronoi partition)." @default.
- W2157665775 created "2016-06-24" @default.
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- W2157665775 date "2013-12-31" @default.
- W2157665775 modified "2023-09-27" @default.
- W2157665775 title "Separating a Voronoi Diagram via Local Search" @default.
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