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(m 4 n) algorithm, which is the first polynomial time algorithm for this problem. We also present an Õ(m 3 n) 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.
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Kavitha, T., Mehlhorn, K. (2005). A Polynomial Time Algorithm for Minimum Cycle Basis in Directed Graphs. In: Diekert, V., Durand, B. (eds) STACS 2005. STACS 2005. Lecture Notes in Computer Science, vol 3404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31856-9_54
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DOI: https://doi.org/10.1007/978-3-540-31856-9_54
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24998-6
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