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