Geometric Set Cover and Hitting Sets for Polytopes in $R^3$

Abstract

Suppose we are given a finite set of points P in R and a collection of polytopes T that are all translates of the same polytope T . We consider two problems in this paper. The first is the set cover problem where we want to select a minimal number of polytopes from the collection T such that their union covers all input points P . The second problem that we consider is finding a hitting set for the set of polytopes T , that is, we want to select a minimal number of points from the input points P such that every given polytope is hit by at least one point. We give the first constant-factor approximation algorithms for both problems. We achieve this by providing an epsilon-net for translates of a polytope in R of size O( 1 ǫ ).

DOI: 10.4230/LIPIcs.STACS.2008.1367

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Cite this paper

@inproceedings{Laue2008GeometricSC, title={Geometric Set Cover and Hitting Sets for Polytopes in \$R^3\$}, author={S{\"{o}ren Laue}, booktitle={STACS}, year={2008} }