5 research outputs found

    Approximating Minimum-Cost k-Node Connected Subgraphs via Independence-Free Graphs

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    We present a 6-approximation algorithm for the minimum-cost kk-node connected spanning subgraph problem, assuming that the number of nodes is at least k3(k−1)+kk^3(k-1)+k. We apply a combinatorial preprocessing, based on the Frank-Tardos algorithm for kk-outconnectivity, to transform any input into an instance such that the iterative rounding method gives a 2-approximation guarantee. This is the first constant-factor approximation algorithm even in the asymptotic setting of the problem, that is, the restriction to instances where the number of nodes is lower bounded by a function of kk.Comment: 20 pages, 1 figure, 28 reference

    Approximating minimum cost connectivity problems

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    We survey approximation algorithms of connectivity problems. The survey presented describing various techniques. In the talk the following techniques and results are presented. 1)Outconnectivity: Its well known that there exists a polynomial time algorithm to solve the problems of finding an edge k-outconnected from r subgraph [EDMONDS] and a vertex k-outconnectivity subgraph from r [Frank-Tardos] . We show how to use this to obtain a ratio 2 approximation for the min cost edge k-connectivity problem. 2)The critical cycle theorem of Mader: We state a fundamental theorem of Mader and use it to provide a 1+(k-1)/n ratio approximation for the min cost vertex k-connected subgraph, in the metric case. We also show results for the min power vertex k-connected problem using this lemma. We show that the min power is equivalent to the min-cost case with respect to approximation. 3)Laminarity and uncrossing: We use the well known laminarity of a BFS solution and show a simple new proof due to Ravi et al for Jain\u27s 2 approximation for Steiner network
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