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

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 minimumweight 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 show how to obtai...

• Type: Conference
• Year: 2006
• Where: APPROX
• Authors: Christoph Ambühl, Thomas Erlebach, Matús Mihalák, Marc Nunkesser
• Keywords: Algorithms, APPROX 2006, Dominating Set Problem, Unit Disk, Unit Disk Graphs