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- W2806095013 abstract "Finding cohesive subgraphs in a network is a well-known problem in graph theory. Several alternative formulations of cohesive subgraph have been proposed, a notable example being s-club, which is a subgraph where each vertex is at distance at most s to the others. Here we consider the problem of covering a given graph with the minimum number of s-clubs. We study the computational and approximation complexity of this problem, when s is equal to 2 or 3. First, we show that deciding if there exists a cover of a graph with three 2-clubs is NP-complete, and that deciding if there exists a cover of a graph with two 3-clubs is NP-complete. Then, we consider the approximation complexity of covering a graph with the minimum number of 2-clubs and 3-clubs. We show that, given a graph (G=(V,E)) to be covered, covering G with the minimum number of 2-clubs is not approximable within factor (O(|V|^{1/2 -varepsilon })), for any (varepsilon >0), and covering G with the minimum number of 3-clubs is not approximable within factor (O(|V|^{1 -varepsilon })), for any (varepsilon >0). On the positive side, we give an approximation algorithm of factor (2|V|^{1/2}log ^{3/2} |V|) for covering a graph with the minimum number of 2-clubs." @default.
- W2806095013 created "2018-06-13" @default.
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- W2806095013 date "2018-01-01" @default.
- W2806095013 modified "2023-09-25" @default.
- W2806095013 title "Covering with Clubs: Complexity and Approximability" @default.
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- W2806095013 doi "https://doi.org/10.1007/978-3-319-94667-2_13" @default.
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