An Approximation Algorithm for the Minimum Weight Vertex-Connectivity Problem in Complete Graphs with Sharpened Triangle Inequality
نویسندگان
چکیده
Consider a complete graph G with the edge weights satisfying the β-sharpened triangle inequality: weight(u, v) ≤ β(weight(u, x)+ weight(x, v)), for 1/2 ≤ β < 1. We study the NP-hard problem of finding a minimum weight spanning subgraph of G which is k-vertex-connected, k ≥ 2, and give a detailed analysis of an approximation quadratic-time algorithm whose performance ratio is β 1−β . The algorithm is derived from the one presented by Böckenhauer et al. in [3] for the k-edge connectivity problem on graphs satisfying the βsharpened triangle inequality.
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