Geometric Set Cover and Hitting Sets for Polytopes in $R^3$
| dc.creator | Laue, Sören | |
| dc.date | 2008-02-20 | |
| dc.date.accessioned | 2026-07-07T09:22:04Z | |
| dc.date.available | 2026-07-07T09:22:04Z | |
| dc.description | 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 $\bigO(\frac{1{ε)$. | |
| dc.identifier | https://arxiv.org/abs/0802.2861 | |
| dc.identifier | http://arxiv.org/abs/0802.2861 | |
| dc.identifier | Dans Proceedings of the 25th Annual Symposium on the Theoretical Aspects of Computer Science - STACS 2008, Bordeaux : France (2008) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155245 | |
| dc.subject | Computational Geometry | |
| dc.title | Geometric Set Cover and Hitting Sets for Polytopes in $R^3$ | |
| dc.type | text |