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On a Special Co-cycle Basis of Graphs

Kavitha, Telikepalli (2008) On a Special Co-cycle Basis of Graphs. In: 11th Scandinavian Workshop on Algorithm Theory (SWAT 2008), JUL 02-04, 2008, Gothenburg.

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In this paper we consider the problems of computing a minimum co-cycle basis and a minimum weakly fundamental co-cycle basis of a directed graph G. A co-cycle in G corresponds to a vertex partition (S,V ∖ S) and a { − 1,0,1} edge incidence vector is associated with each co-cycle. The vector space over ℚ generated by these vectors is the co-cycle space of G. Alternately, the co-cycle space is the orthogonal complement of the cycle space of G. The minimum co-cycle basis problem asks for a set of co-cycles that span the co-cycle space of G and whose sum of weights is minimum. Weakly fundamental co-cycle bases are a special class of co-cycle bases, these form a natural superclass of strictly fundamental co-cycle bases and it is known that computing a minimum weight strictly fundamental co-cycle basis is NP-hard. We show that the co-cycle basis corresponding to the cuts of a Gomory-Hu tree of the underlying undirected graph of G is a minimum co-cycle basis of G and it is also weakly fundamental.

Item Type: Conference Paper
Publisher: Springer
Additional Information: Copyright of this article belongs to Springer.
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Date Deposited: 26 Mar 2010 06:28
Last Modified: 19 Sep 2010 05:58
URI: http://eprints.iisc.ac.in/id/eprint/26548

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