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Separating a Voronoi Diagram via Local Search Bhattiprolu, Vijay V. S. P. Har-Peled, Sariel Separators Local search Approximation Voronoi diagrams Delaunay triangulation Meshing Geometric hitting set 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Vijay V. S. P. Bhattiprolu and Sariel Har-Peled 2016 Is Part Of LIPIcs, Volume 51, 32nd International Symposium on Computational Geometry (SoCG 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2016.18 urn:nbn:de:0030-drops-59107 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.18 eng https://creativecommons.org/licenses/by/3.0/legalcode