A note on multicovering with disks

Reuven Bar-Yehuda, Dror Rawitz

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


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)α, for some constant α. 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 αkmax-approximation algorithm for Disk Multicover, where kmax is the maximum covering requirement of a point, and a (3 αK+ε)-approximation algorithm for Polygon Disk Multicover.

Original languageEnglish
Pages (from-to)394-399
Number of pages6
JournalComputational Geometry: Theory and Applications
Issue number3
StatePublished - Apr 2013
Externally publishedYes


  • Approximation algorithms
  • Disk cover
  • Multicovering


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