Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric Set Cover and Hitting Sets for Polytopes in $R^3$   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 $\bigO(\frac{1{\epsilon)$.

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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
2
The categories of this paper are: math
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph