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Geometric Set Cover and Hitting Sets for Polytopes in R³ Lauen, Sören Computational Geometry Epsilon-Nets Set Cover Hitting Sets Suppose we are given a finite set of points $P$ in $R^3$ and a collection of polytopes $mathcal{T}$ 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 $mathcal{T}$ 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 $mathcal{T}$, 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 $R^3$ of size $\bigO(frac{1{epsilon)$. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Sören Lauen 2008 Is Part Of LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2008.1367 urn:nbn:de:0030-drops-13675 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1367 eng https://creativecommons.org/licenses/by-nd/3.0/legalcode