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• W2052656799 abstract "We give approximation algorithms for the Survivable Network problem. The input consists of a graph G = ( V,E ) with edge/node-costs, a node subset S ⊆ V , and connectivity requirements { r ( s,t ): s,t ∈ T ⊆ V }. The goal is to find a minimum cost subgraph H of G that for all s,t ∈ T contains r ( s,t ) pairwise edge-disjoint st -paths such that no two of them have a node in S ∖ { s,t } in common. Three extensively studied particular cases are: Edge-Connectivity Survivable Network ( S = ∅), Node-Connectivity Survivable Network ( S = V ), and Element-Connectivity Survivable Network ( r ( s,t ) = 0 whenever s ∈ S or t ∈ S ). Let k = max s,t ∈ T r ( s,t ). In Rooted Survivable Network, there is s ∈ T such that r ( u,t ) = 0 for all u ≠ s , and in the Subset k -Connected Subgraph problem r ( s,t ) = k for all s,t ∈ T . For edge-costs, our ratios are O ( k log k ) for Rooted Survivable Network and O ( k 2 log k ) for Subset k -Connected Subgraph. This improves the previous ratio O ( k 2 log n ), and for constant values of k settles the approximability of these problems to a constant. For node-costs, our ratios are as follows. — O ( k log | T |) for Element-Connectivity Survivable Network, matching the best known ratio for Edge-Connectivity Survivable Network. — O ( k 2 log | T |) for Rooted Survivable Network and O ( k 3 log | T |) for Subset k -Connected Subgraph, improving the ratio O ( k 8 log 2 | T |). — O ( k 4 log 2 | T |) for Survivable Network; this is the first nontrivial approximation algorithm for the node-costs version of the problem." @default.
• W2052656799 created "2016-06-24" @default.
• W2052656799 creator A5003622145 @default.
• W2052656799 date "2012-12-01" @default.
• W2052656799 modified "2023-10-18" @default.
• W2052656799 title "Approximating minimum-cost connectivity problems via uncrossable bifamilies" @default.
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• W2052656799 doi "https://doi.org/10.1145/2390176.2390177" @default.
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