License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2016.18
URN: urn:nbn:de:0030-drops-59107
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/5910/
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Bhattiprolu, Vijay V. S. P. ; Har-Peled, Sariel

Separating a Voronoi Diagram via Local Search

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LIPIcs-SoCG-2016-18.pdf (0.8 MB)

Abstract

Given a set P of n points in R^d , we show how to insert a set Z of O(n^(1-1/d)) additional points, such that P can be broken into two sets P1 and P2 , of roughly equal size, such that in the Voronoi diagram V(P u Z), the cells of P1 do not touch the cells of P2; that is, Z separates P1 from P2 in the Voronoi diagram (and also in the dual Delaunay triangulation). In addition, given such a partition (P1,P2) of P , we present an approximation algorithm to compute a minimum size separator realizing this partition. We also present a simple local search algorithm that is a PTAS for approximating the optimal Voronoi partition.

BibTeX - Entry

@InProceedings{bhattiprolu_et_al:LIPIcs:2016:5910,
  author =	{Vijay V. S. P. Bhattiprolu and Sariel Har-Peled},
  title =	{{Separating a Voronoi Diagram via Local Search}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{18:1--18:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{S{\'a}ndor Fekete and Anna Lubiw},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5910},
  URN =		{urn:nbn:de:0030-drops-59107},
  doi =		{10.4230/LIPIcs.SoCG.2016.18},
  annote =	{Keywords: Separators, Local search, Approximation, Voronoi diagrams, Delaunay triangulation, Meshing, Geometric hitting set}
}

Keywords: Separators, Local search, Approximation, Voronoi diagrams, Delaunay triangulation, Meshing, Geometric hitting set
Collection: 32nd International Symposium on Computational Geometry (SoCG 2016)
Issue Date: 2016
Date of publication: 10.06.2016

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