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

Thomas Erlebach, Matúš Mihalák

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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)
Number of pages12
Publication statusPublished - 2009
Externally publishedYes

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