2005 | OriginalPaper | Buchkapitel
No, Coreset, No Cry
verfasst von : Sariel Har-Peled
Erschienen in: FSTTCS 2004: Foundations of Software Technology and Theoretical Computer Science
Verlag: Springer Berlin Heidelberg
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We show that coresets do not exist for the problem of 2-slabs in
${\mathbb R}^{3}$
, thus demonstrating that the natural approach for solving approximately this problem efficiently is infeasible. On the positive side, for a point set
P
in
${\mathbb R}^{3}$
, we describe a near linear time algorithm for computing a (1+
ε
)-approximation to the minimum width 2-slab cover of
P
. This is a first step in providing an efficient approximation algorithm for the problem of covering a point set with
k
-slabs.