Approximating graph-constrained max-cut
Math. Program.(2017)
摘要
n instance of the graph-constrained max-cut ( 𝖦𝖢𝖬𝖢 ) problem consists of (i) an undirected graph G=(V,E) and (ii) edge-weights c:V ()2→ℝ_+ on a complete undirected graph. The objective is to find a subset S ⊆ V of vertices satisfying some graph-based constraint in G that maximizes the weight ∑ _u∈ S, v∉S c_uv of edges in the cut (S,V∖ S) . The types of graph constraints we can handle include independent set, vertex cover, dominating set and connectivity. Our main results are for the case when G is a graph with bounded treewidth, where we obtain a 1/2 -approximation algorithm. Our algorithm uses an LP relaxation based on the Sherali–Adams hierarchy. It can handle any graph constraint for which there is a dynamic program of a specific form. Using known decomposition results, these imply essentially the same approximation ratio for 𝖦𝖢𝖬𝖢 under constraints such as independent set, dominating set and connectivity on a planar graph G .
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关键词
90C27 Combinatorial Optimization,68W25 Approximation Algorithm
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