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Improved Approximation Algorithms for Min-Cost Connectivity Augmentation Problems

  • Zeev NutovEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9691)

Abstract

A graph G is k-connected if it has k internally-disjoint st-paths for every pair st of nodes. Given a root s and a set T of terminals is k-\((s,T)\)-connected if it has k internally-disjoint st-paths for every \(t \in T\). We consider two well studied min-cost connectivity augmentation problems, where we are given an integer \(k \ge 0\), a graph \(G=(V,E)\), and and an edge set F on V with costs. The goal is to compute a minimum cost edge set \(J \subseteq F\) such that \(G+J\) has connectivity \(k+1\). In the k -Connectivity Augmentation problem G is k-connected and \(G+J\) should be \((k+1)\)-connected. In the \(k\)-\((s,T)\) -Connectivity Augmentation problem G is k-\((s,T)\)-connected and \(G+J\) should be \((k+1)\)-(sT)-connected.

For the k -Connectivity Augmentation problem we obtain the following results. For \(n \ge 3k-5\), we obtain approximation ratios 3 for directed graphs and 4 for undirected graphs,improving the previous ratio 5 of [26]. For directed graphs and \(k=1\), or \(k=2\) and n odd, we further improve to 2.5 the previous ratios 3 and 4, respectively.

For the undirected \(2\)-\((s,T)\) -Connectivity Augmentation problem we achieve ratio \(4\frac{2}{3}\), improving the previous best ratio 12 of [24]. For the special case when all the edges in F are incident to s, we give a polynomial time algorithm, improving the ratio \(4\frac{17}{30}\) of [21, 25] for this variant.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.The Open University of IsraelRa’ananaIsrael

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