### 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.

Original language | English |
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Title of host publication | Proceedings of the 9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX) |

Pages | 3-14 |

Number of pages | 12 |

DOIs | |

Publication status | Published - 2006 |

Externally published | Yes |

## Cite this

Ambühl, C., Erlebach, T., Mihalák, M., & Nunkesser, M. (2006). Constant-Factor Approximation for Minimum-Weight (Connected) Dominating Sets in Unit Disk Graphs. In

*Proceedings of the 9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX)*(pp. 3-14) https://doi.org/10.1007/11830924_3