### Geometric Set Cover and Hitting Sets for Polytopes in RÂ³

SÃ¶Ren Lauen
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...