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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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References:
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