A polynomial time algorithm for minimum cycle basis in directed graphs

Authors:
Telikepalli Kavitha;Kurt Mehlhorn
Affiliations:
Max-Planck-Institut für Informatik, Saarbrücken, Germany;Max-Planck-Institut für Informatik, Saarbrücken, Germany
Venue:
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Year:
2005

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Abstract

We consider the problem of computing a minimum cycle basis in a directed graph G with m arcs and n vertices. The arcs of G have non-negative weights assigned to them. We give an Õ(m4n) algorithm, which is the first polynomial time algorithm for this problem. We also present an Õ(m3n) randomized algorithm. The problem of computing a minimum cycle basis in an undirected graph has been well-studied. However, it is not known if an efficient algorithm for undirected graphs automatically translates to an efficient algorithm for directed graphs.