A (4+ε)-approximation for the minimum-weight dominating set problem in unit disk graphs

  • Authors:

  • Thomas Erlebach;Matúš Mihalák

  • Affiliations:

  • Department of Computer Science, University of Leicester, England;Institute of Theoretical Computer Science, ETH Zurich, Switzerland

  • Venue:
  • WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

Abstract

We present a (4+ε)-approximation algorithm for the problem of computing a minimum-weight dominating set in unit disk graphs, where ε is an arbitrarily small constant. The previous best known approximation ratio was 5+ε. The main result of this paper is a 4-approximation algorithm for the problem restricted to constant-size areas. To obtain the (4+ε)-approximation algorithm for the unrestricted problem, we then follow the general framework from previous constant-factor approximations for the problem: We consider the problem in constant-size areas, and combine the solutions obtained by our 4-approximation algorithm for the restricted case to get a feasible solution for the whole problem. Using the shifting technique (selecting a best solution from several considered partitionings of the problem into constant-size areas) we obtain the claimed (4+ε)-approximation algorithm. By combining our algorithm with a known algorithm for node-weighted Steiner trees, we obtain a 7.875-approximation for the minimum-weight connected dominating set problem in unit disk graphs.