TY - GEN

T1 - Covering points by unit disks of fixed location

AU - Carmi, Paz

AU - Katz, Matthew J.

AU - Lev-Tov, Nissan

PY - 2007/1/1

Y1 - 2007/1/1

N2 - Given a set P of points in the plane, and a set D of unit disks of fixed location, the discrete unit disk cover problem is to find a minimum-cardinality subset D′ ⊆ D that covers all points of 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 NP-hard, but while the general set cover problem is not approximate within clog |P|, for some constant c, the discrete unit disk cover problem was shown to admit a constant-factor 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 4-approximation that we devise for the subproblem where the points of V are located below a line l and contained in the subset of disks of D centered above l. This problem is of independent interest.

AB - Given a set P of points in the plane, and a set D of unit disks of fixed location, the discrete unit disk cover problem is to find a minimum-cardinality subset D′ ⊆ D that covers all points of 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 NP-hard, but while the general set cover problem is not approximate within clog |P|, for some constant c, the discrete unit disk cover problem was shown to admit a constant-factor 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 4-approximation that we devise for the subproblem where the points of V are located below a line l and contained in the subset of disks of D centered above l. This problem is of independent interest.

UR - http://www.scopus.com/inward/record.url?scp=38149068205&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-77120-3_56

DO - 10.1007/978-3-540-77120-3_56

M3 - Conference contribution

AN - SCOPUS:38149068205

SN - 9783540771180

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 644

EP - 655

BT - Algorithms and Computation - 18th International Symposium, ISAAC 2007, Proceedings

PB - Springer Verlag

T2 - 18th International Symposium on Algorithms and Computation, ISAAC 2007

Y2 - 17 December 2007 through 19 December 2007

ER -