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A better constant-factor approximation for weighted dominating set in unit disk graph. (English) Zbl 1184.05090
Summary: This paper presents a \((10+\varepsilon)\)-approximation algorithm to compute minimum-weight connected dominating set (MWCDS) in unit disk graph. MWCDS is to select a vertex subset with minimum weight for a given unit disk graph, such that each vertex of the graph is contained in this subset or has a neighbor in this subset. Besides, the subgraph induced by this vertex subset is connected. Our algorithm is composed of two phases: the first phase computes a dominating set, which has approximation ratio \(6 + \varepsilon\) (\(\varepsilon\) is an arbitrary positive number), while the second phase connects the dominating sets computed in the first phase, which has approximation ratio 4.

05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
05C22 Signed and weighted graphs
Full Text: DOI
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