A (4 + epsilon)-Approximation for the Minimum-Weight Dominating Set Problem in Unit Disk Graphs

Thomas Erlebach, Matúš Mihalák

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

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 languageEnglish
Title of host publicationProceedings of the 7th International Workshop on Approximation and Online Algorithms (WAOA)
Pages135-146
Number of pages12
DOIs
Publication statusPublished - 2009
Externally publishedYes

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