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:
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.
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Laekhanukit, B. (2011). An Improved Approximation Algorithm for Minimum-Cost Subset k-Connectivity. In: Aceto, L., Henzinger, M., Sgall, J. (eds) Automata, Languages and Programming. ICALP 2011. Lecture Notes in Computer Science, vol 6755. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22006-7_2
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DOI: https://doi.org/10.1007/978-3-642-22006-7_2
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