1. Improved approximation ratio for covering pliable set families
- Author
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Nutov, Zeev
- Subjects
Computer Science - Data Structures and Algorithms - Abstract
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 set families, that have much weaker uncrossing properties. In this paper we will refine their analysis and show an approximation ratio of $10$. This also improves approximation ratios for several variants of the Capacitated $k$-Edge Connected Spanning Subgraph problem., Comment: arXiv admin note: text overlap with arXiv:2307.08270
- Published
- 2024