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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Veröffentlicht in:Theoretical computer science Jg. 527; S. 50 - 60
Hauptverfasser: Ghasemi, Taha, Razzazi, Mohammadreza
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 27.03.2014
Schlagworte:
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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Zusammenfassung: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