Pruning 2-Connected Graphs

13 years 5 months ago

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Given an edge-weighted undirected graph G with a speciﬁed set of terminals, let the density of any subgraph be the ratio of its weight/cost to the number of terminals it contains. If G is 2-connected, does it contain smaller 2-connected subgraphs of density comparable to that of G? We answer this question in the afﬁrmative by giving an algorithm to prune G and ﬁnd such subgraphs of any desired size, at the cost of only a logarithmic increase in density (plus a small additive factor). We apply the pruning techniques to give algorithms for two NP-Hard problems on ﬁnding large 2-vertex-connected subgraphs of low cost; no previous approximation algorithm was known for either problem. In the k-2VC problem, we are given an undirected graph G with edge costs and an integer k; the goal is to ﬁnd a minimum-cost 2-vertex-connected subgraph of G containing at least k vertices. In the Budget-2VC problem, we are given the graph G with edge costs, and a budget B; the goal is to ﬁnd a 2-...

Chandra Chekuri, Nitish Korula

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