### Abstract

We present a (4 + e)-approximation algorithm for the problem of computing a minimum-weight dominating set in unit disk graphs, where e is an arbitrarily small constant. The previous best known approximation ratio was 5 + e. The main result of this paper is a 4-approximation algorithm for the problem restricted to constant-size areas. To obtain the (4 + e)-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 + e)-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.

Original language | English |
---|---|

Title of host publication | Proceedings of the 7th International Workshop on Approximation and Online Algorithms (WAOA) |

Pages | 135-146 |

Number of pages | 12 |

DOIs | |

Publication status | Published - 2009 |

Externally published | Yes |

## Cite this

Erlebach, T., & Mihalák, M. (2009). A (4 + epsilon)-Approximation for the Minimum-Weight Dominating Set Problem in Unit Disk Graphs. In

*Proceedings of the 7th International Workshop on Approximation and Online Algorithms (WAOA)*(pp. 135-146) https://doi.org/10.1007/978-3-642-12450-1_13