A Better Approximation Ratio for the Minimum k-Edge-Connected Spanning Subgraph Problem
نویسنده
چکیده
Consider the minimum k-edge-connected spanning subgraph problem: given a positive integer k and a k-edge-connected graph G, nd a k-edge-connected spanning subgraph of G with minimum number of edges. This problem is known to be NP-complete. Khuller and Raghavachari presented the rst algorithm with a performance ratio smaller than 2 for all k. They proved an upper bound of 1.85 for the performance ratio of their algorithm. We improve their analysis, proving that the performance ratio of their algorithm is smaller than 1.7 for large enough k, and that it is at most 1.75 for all k. Our analysis improves the best known ratios for any xed k 4, in particular, for k = 4 from 1.75 to 1.65, and for k = 5 from 1.733... to 1.68. Last, we show that the minimum k-edge-connected spanning subgraph problem is MAX SNP-hard, even for k = 2.
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