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- W2292508615 abstract "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-vertex-connected subgraph H of G with total edge cost at most B that maximizes the number of vertices in H. We describe an O(lognlogk) approximation for the k-2VC problem, and a bicriteria approximation for the Budget-2VC problem that gives an O( 1 log 2 n) approximation, while violating the budget by a factor of at most 3 + ǫ." @default.
- W2292508615 created "2016-06-24" @default.
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- W2292508615 date "2008-01-01" @default.
- W2292508615 modified "2023-09-27" @default.
- W2292508615 title "Pruning 2-Connected Graphs (Extended Abstract)" @default.
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