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- W46202281 abstract "The minimum-cost subset k-connected subgraph problem is a cornerstone problem in the area of network design with vertex connectivity requirements. In this problem, we are given a graph G = (V,E) with costs on edges and a set of terminals T. The goal is to find a minimum cost subgraph such that every pair of terminals are connected by k openly (vertex) disjoint paths. In this paper, we present an approximation algorithm for the subset k-connected subgraph problem which improves on the previous best approximation guarantee of O(k 2logk) by Nutov (FOCS 2009). Our approximation guarantee, α(|T |), depends upon the number of terminals: $$ alpha(|T|) = begin{cases} O(|T|^2) &mbox{if } |T| < 2k O(k log^2 k) & mbox{if } 2kle |T| < k^2 O(k log k) & mbox{if } |T| ge k^2 end{cases} $$ So, when the number of terminals is large enough, the approximation guarantee improves significantly. Moreover, we show that, given an approximation algorithm for |T | = k, we can obtain almost the same approximation guarantee for any instances with |T | > k. This suggests that the hardest instances of the problem are when |T | ≈ k." @default.
- W46202281 created "2016-06-24" @default.
- W46202281 creator A5005632876 @default.
- W46202281 date "2011-01-01" @default.
- W46202281 modified "2023-09-24" @default.
- W46202281 title "An Improved Approximation Algorithm for Minimum-Cost Subset k-Connectivity" @default.
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- W46202281 doi "https://doi.org/10.1007/978-3-642-22006-7_2" @default.
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