Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Selecting forwarding neighbors in wireless ad hoc networks
Mobile Networks and Applications - Discrete algorithms and methods for mobile computing and communications
Improved approximation algorithms for geometric set cover
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Approximating geometric coverage problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
PTAS for geometric hitting set problems via local search
Proceedings of the twenty-fifth annual symposium on Computational geometry
Homogeneous 2-hop broadcast in 2D
Computational Geometry: Theory and Applications
A Scheme for Computing Minimum Covers within Simple Regions
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Practical Discrete Unit Disk Cover Using an Exact Line-Separable Algorithm
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
PTAS for weighted set cover on unit squares
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Optimal cover of points by disks in a simple polygon
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
On the discrete unit disk cover problem
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Minimum-cost linear coverage by sensors with adjustable ranges
WASA'11 Proceedings of the 6th international conference on Wireless algorithms, systems, and applications
Wireless coverage via dynamic programming
WASA'11 Proceedings of the 6th international conference on Wireless algorithms, systems, and applications
Wireless coverage with disparate ranges
MobiHoc '11 Proceedings of the Twelfth ACM International Symposium on Mobile Ad Hoc Networking and Computing
Optimal Cover of Points by Disks in a Simple Polygon
SIAM Journal on Computing
Providing and finding k-road-coverage efficiently in wireless sensor networks
Wireless Communications & Mobile Computing
| Hi-index | 0.00 |
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 approximable within c log |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 P are located below a line l and contained in the subset of disks of D centered above l. This problem is of independent interest.