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New algorithms to compute the strength of a graph

Jérôme Galtier 1
1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : We investigate the problem of computing the strength of a graph. We describe in this article the first polyhedral formulation for the weighted strength in polynomial size of the problem, that is O(mn), where n is the number of vertices and m the number of edges. Moreover, we describe a surprisingly simple FPTAS that gives the strength within 1+epsilon in time O(m log^2(n) log(m/n)/epsilon^2) and space O(m), outperforming by a factor of roughly min(n\sqrt{m},n^5/3) the best known exact algorithm of Trubin associated with the Goldberg and Rao maxflow algorithm for that problem, and of roughly sigma(G) the FPTAS of Plotkin, Shmoys, and Tardos.
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https://hal.inria.fr/inria-00305560
Contributor : Jerome Galtier <>
Submitted on : Tuesday, July 29, 2008 - 4:09:56 PM
Last modification on : Monday, October 12, 2020 - 10:30:12 AM
Long-term archiving on: : Wednesday, March 29, 2017 - 3:09:17 PM

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  • HAL Id : inria-00305560, version 2

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Jérôme Galtier. New algorithms to compute the strength of a graph. [Research Report] RR-6592, INRIA. 2008, pp.17. ⟨inria-00305560v2⟩

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