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A Fast Algorithm for Computing Steiner Edge Connectivity

Cole, Richard and Hariharan, Ramesh (2003) A Fast Algorithm for Computing Steiner Edge Connectivity. In: Thirty-Fifth Annual ACM Symposium on Theory of Computing, June 9–11, 2003, San Diego, California, USA, pp. 167-176.


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Given an undirected graph or an Eulerian directed graph G and a subset S of its vertices, we show how to determine the edge connectivity C of the vertices in S in time O(C3 n log n+m). This algorithm is based on an efficient construction of tree packings which generalizes Edmonds' Theorem. These packings also yield a characterization of all minimal Steiner cuts of size C from which an efficient data structure for maintaining edge connectivity between vertices in S under edge insertion can be obtained. This data structure enables the efficient construction of a cactus tree for representing significant C-cuts among these vertices, called C-separations, in the same time bound. In turn, we use the cactus tree to give a fast implementation of an approximation algorithm for the Survivable Network Design problem due to Williamson, Goemans, Mihail and Vazirani.

Item Type: Conference Paper
Publisher: ACM Press
Additional Information: ©ACM,2003.This is the author's version of the work.It is posted here by permission of ACM for your personal use.Not for redistribution.The definitive version was published in Proceedings of the thirty-fifth ACM symposium on Theory of computing,2003 http://doi.acm.org/10.1145/780542.780568
Keywords: Steiner points;cactus trees;edge-connectivity;algorithms
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Date Deposited: 09 Jun 2004
Last Modified: 19 Sep 2010 04:12
URI: http://eprints.iisc.ac.in/id/eprint/261

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