Constant-factor approximation for minimum-weight (connected) dominating sets in unit disk graphs

  • Authors:

  • Christoph Ambühl;Thomas Erlebach;Matúš Mihalák;Marc Nunkesser

  • Affiliations:

  • Department of Computer Science, University of Liverpool;Department of Computer Science, University of Liverpool;Department of Computer Science, University of Liverpool;Institute of Theoretical Computer Science, ETH Zürich

  • Venue:
  • APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
  • Year:
  • 2006

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Abstract

For a given graph with weighted vertices, the goal of the minimum-weight dominating set problem is to compute a vertex subset of smallest weight such that each vertex of the graph is contained in the subset or has a neighbor in the subset. A unit disk graph is a graph in which each vertex corresponds to a unit disk in the plane and two vertices are adjacent if and only if their disks have a non-empty intersection. We present the first constant-factor approximation algorithm for the minimum-weight dominating set problem in unit disk graphs, a problem motivated by applications in wireless ad-hoc networks. The algorithm is obtained in two steps: First, the problem is reduced to the problem of covering a set of points located in a small square using a minimum-weight set of unit disks. Then, a constant-factor approximation algorithm for the latter problem is obtained using enumeration and dynamic programming techniques exploiting the geometry of unit disks. Furthermore, we also show how to obtain a constant-factor approximation algorithm for the minimum-weight connected dominating set problem in unit disk graphs.