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A \(5+\varepsilon\)-approximation algorithm for minimum weighted dominating set in unit disk graph. (English) Zbl 1162.68042
Summary: We study the minimum weight dominating set problem in weighted unit disk graph, and give a polynomial time algorithm with approximation ratio \(5+\varepsilon \), improving the previous best result of \(6+\varepsilon \) in [X. Gao, Y. Huang, Z. Zhang and W. Wu, “\((6 + \epsilon )\)-approximation for minimum weight dominating set in unit disk graphs”, Lect. Notes Comput. Sci. 5092, 551–557 (2008; Zbl 1148.05310)]. Combining the common technique used in the above mentioned reference, we can compute a minimum weight connected dominating set with approximation ratio \(9+\varepsilon \), beating the previously best result of \(10+\varepsilon \) in the same work.

MSC:
68W25 Approximation algorithms
05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
68R10 Graph theory (including graph drawing) in computer science
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