Volume 4835 of the series Lecture Notes in Computer Science pp 644655
Covering Points by Unit Disks of Fixed Location
 Paz CarmiAffiliated withSchool of Computer Science, Carleton University, Ottawa
 , Matthew J. KatzAffiliated withDepartment of Computer Science, BenGurion University, BeerSheva
 , Nissan LevTovAffiliated withDepartment of Computer Science, BenGurion University, BeerSheva
Abstract
Given a set \({\mathcal P}\) of points in the plane, and a set \({\mathcal D}\) of unit disks of fixed location, the discrete unit disk cover problem is to find a minimumcardinality subset \({\mathcal D}' \subseteq {\mathcal D}\) that covers all points of \({\mathcal P}\). This problem is a geometric version of the general set cover problem, where the sets are defined by a collection of unit disks. It is still NPhard, but while the general set cover problem is not approximable within \(c \log {\mathcal P}\), for some constant c, the discrete unit disk cover problem was shown to admit a constantfactor approximation. Due to its many important applications, e.g., in wireless network design, much effort has been invested in trying to reduce the constant of approximation of the discrete unit disk cover problem. In this paper we significantly improve the best known constant from 72 to 38, using a novel approach. Our solution is based on a 4approximation that we devise for the subproblem where the points of \({\mathcal P}\) are located below a line l and contained in the subset of disks of \({\mathcal D}\) centered above l. This problem is of independent interest.
 Title
 Covering Points by Unit Disks of Fixed Location
 Book Title
 Algorithms and Computation
 Book Subtitle
 18th International Symposium, ISAAC 2007, Sendai, Japan, December 1719, 2007. Proceedings
 Pages
 pp 644655
 Copyright
 2007
 DOI
 10.1007/9783540771203_56
 Print ISBN
 9783540771180
 Online ISBN
 9783540771203
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 4835
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
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 Editors
 Authors

 Paz Carmi ^{(1)}
 Matthew J. Katz ^{(2)}
 Nissan LevTov ^{(2)}
 Author Affiliations

 1. School of Computer Science, Carleton University, Ottawa, Canada
 2. Department of Computer Science, BenGurion University, BeerSheva, Israel
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