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...

Full description

Saved in:

Bibliographic Details
Published in:	Theoretical computer science Vol. 527; pp. 50 - 60
Main Authors:	Ghasemi, Taha, Razzazi, Mohammadreza
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 27.03.2014
Subjects:	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
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	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