A PTAS for the cardinality constrained covering with unit balls

In this paper, we address the cardinality constrained covering with unit balls problem: given a positive integer L and a set of n points in Rd, partition them into a minimum number of parts such that each part contains at most L points and it can be covered by a unit ball of the given ℓp metric. Dev...

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Vydáno v:	Theoretical computer science Ročník 527; s. 50 - 60
Hlavní autoři:	Ghasemi, Taha, Razzazi, Mohammadreza
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier B.V 27.03.2014
Témata:	Capacitated covering Cardinality constrained covering Computational geometry Covering with disks Fully polynomial time approximation algorithm Computational geometry Fully polynomial time approximation algorithm Capacitated covering Cardinality constrained covering Covering with disks
ISSN:	0304-3975, 1879-2294
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Popis
Shrnutí:	In this paper, we address the cardinality constrained covering with unit balls problem: given a positive integer L and a set of n points in Rd, partition them into a minimum number of parts such that each part contains at most L points and it can be covered by a unit ball of the given ℓp metric. Developing a constant-factor approximation algorithm for this problem is an old open problem. By proving a structural property in the problem and applying the shifting strategy and dynamic programming, we derive the first (1+ε)d-approximation nO(1/εd)-time algorithm for this problem when d is a fixed constant.
ISSN:	0304-3975 1879-2294
DOI:	10.1016/j.tcs.2014.01.026