Computational geometry: an introduction
Computational geometry: an introduction
Plane-sweep algorithms for intersecting geometric figures
Communications of the ACM
Local ratio: A unified framework for approximation algorithms. In Memoriam: Shimon Even 1935-2004
ACM Computing Surveys (CSUR)
Minimum-cost coverage of point sets by disks
Proceedings of the twenty-second annual symposium on Computational geometry
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
On the set multi-cover problem in geometric settings
Proceedings of the twenty-fifth annual symposium on Computational geometry
Polynomial time approximation schemes for base station coverage with minimum total radii
Computer Networks: The International Journal of Computer and Telecommunications Networking
Multi cover of a polygon minimizing the sum of areas
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Geometric clustering to minimize the sum of cluster sizes
ESA'05 Proceedings of the 13th annual European conference on Algorithms
A constant-factor approximation for multi-covering with disks
Proceedings of the twenty-ninth annual symposium on Computational geometry
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In the Disk Multicover problem the input consists of a set P of n points in the plane, where each point p@?P has a covering requirement k(p), and a set B of m base stations, where each base station b@?B has a weight w(b). If a base station b@?B is assigned a radius r(b), it covers all points in the disk of radius r(b) centered at b. The weight of a radii assignment r:B-R is defined as @?"b"@?"Bw(b)r(b)^@a, for some constant @a. A feasible solution is an assignment such that each point p is covered by at least k(p) disks, and the goal is to find a minimum weight feasible solution. The Polygon Disk Multicover problem is a closely related problem, in which the set P is a polygon (possibly with holes), and the goal is to find a minimum weight radius assignment that covers each point in P at least K times. We present a 3^@ak"m"a"x-approximation algorithm for Disk Multicover, where k"m"a"x is the maximum covering requirement of a point, and a (3^@aK+@e)-approximation algorithm for Polygon Disk Multicover.