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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| Vydané v: | Theoretical computer science Ročník 527; s. 50 - 60 |
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Elsevier B.V
27.03.2014
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Razzazi, Mohammadreza Ghasemi, Taha |
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| Keywords | Computational geometry Fully polynomial time approximation algorithm Capacitated covering Cardinality constrained covering Covering with disks |
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| SubjectTerms | Capacitated covering Cardinality constrained covering Computational geometry Covering with disks Fully polynomial time approximation algorithm |
| Title | A PTAS for the cardinality constrained covering with unit balls |
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