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Reports (Research Report) Year : 2008

New algorithms to compute the strength of a graph


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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Dates and versions

inria-00305560 , version 1 (24-07-2008)
inria-00305560 , version 2 (29-07-2008)


  • HAL Id : inria-00305560 , version 2


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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