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Communication Dans Un Congrès Année : 2022

Approximating k-Edge-Connected Spanning Subgraphs via a Near-Linear Time LP Solver

Résumé

In the k-edge-connected spanning subgraph (kECSS) problem, our goal is to compute a minimum-cost sub-network that is resilient against up to k link failures: Given an n-node m-edge graph with a cost function on the edges, our goal is to compute a minimum-cost k-edge-connected spanning subgraph. This NP-hard problem generalizes the minimum spanning tree problem and is the "uniform case" of a much broader class of survival network design problems (SNDP). A factor of two has remained the best approximation ratio for polynomial-time algorithms for the whole class of SNDP, even for a special case of 2ECSS. The fastest 2-approximation algorithm is however rather slow, taking O(mnk) time [Khuller, Vishkin, STOC'92]. A faster time complexity of O(n 2) can be obtained, but with a higher approximation guarantee of (2k − 1) [Gabow, Goemans, Williamson, IPCO'93]. Our main contribution is an algorithm that (1 + ε)-approximates the optimal fractional solution in Õ(m/ε 2) time (independent of k), which can be turned into a (2 + ε) approximation algorithm that runs in time Õ m ε 2 + k 2 n 1.5 ε 2 for (integral) kECSS; this improves the running time of the aforementioned results while keeping the approximation ratio arbitrarily close to a factor of two.
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Dates et versions

hal-04044666 , version 1 (24-03-2023)

Identifiants

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Parinya Chalermsook, Chien-Chung Huang, Danupon Nanongkai, Thatchaphol Saranurak, Pattara Sukprasert, et al.. Approximating k-Edge-Connected Spanning Subgraphs via a Near-Linear Time LP Solver. 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022), Jul 2022, Paris, France. ⟨10.4230/LIPIcs.ICALP.2022.37⟩. ⟨hal-04044666⟩
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