Constant-Factor Approximation for Minimum-Weight (Connected) Dominating Sets in Unit Disk Graphs

  • Christoph Ambühl
  • Thomas Erlebach
  • Matúš Mihalák
  • Marc Nunkesser
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4110)


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.


Unit Disk Steiner Tree Internal Vertex Unit Disk Graph Disk Cover 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Christoph Ambühl
    • 1
  • Thomas Erlebach
    • 1
  • Matúš Mihalák
    • 1
  • Marc Nunkesser
    • 2
  1. 1.Department of Computer ScienceUniversity of Liverpool 
  2. 2.Institute of Theoretical Computer ScienceETH Zürich 

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