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A classic result of Williamson, Goemans, Mihail, and Vazirani [STOC 1993: 708–717] states that the problem of covering an uncrossable set family by a min-cost edge set admits approximation ratio 2, by a primal-dual algorithm with a reverse delete phase. Recently, Bansal, Cheriyan, Grout, and Ibrahimpur [ICALP 2023: 15:1-15:19] showed that this algorithm achieves approximation ratio 16 for a larger class of so called \(\gamma \) -pliable set families, that have much weaker uncrossing properties. In this paper we will improve the approximation ratio to 10. Using this result and other techniques, we also improve approximation ratios for the following two problems related to the Capacitated k-Edge Connected Spanning Subgraph (Cap- \(k\) -ECSS) problem.

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Improved Approximation Algorithms for Covering Pliable Set Families and Flexible Graph Connectivity

  • 会议论文

  • 发表日期：

    2025年

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  • Zeev Nutov

摘要

A classic result of Williamson, Goemans, Mihail, and Vazirani [STOC 1993: 708–717] states that the problem of covering an uncrossable set family by a min-cost edge set admits approximation ratio 2, by a primal-dual algorithm with a reverse delete phase. Recently, Bansal, Cheriyan, Grout, and Ibrahimpur [ICALP 2023: 15:1-15:19] showed that this algorithm achieves approximation ratio 16 for a larger class of so called \(\gamma \) -pliable set families, that have much weaker uncrossing properties. In this paper we will improve the approximation ratio to 10. Using this result and other techniques, we also improve approximation ratios for the following two problems related to the Capacitated k-Edge Connected Spanning Subgraph (Cap- \(k\) -ECSS) problem.