A polynomial-time algorithm to find the shortest cycle basis of a graph
SIAM Journal on Computing
A Polynomial Time Algorithm to Find the Minimum Cycle Basis of a Regular Matroid
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Minimum Cycle Bases for Network Graphs
Algorithmica
A polynomial time algorithm for minimum cycle basis in directed graphs
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Discrete Applied Mathematics
An improved heuristic for computing short integral cycle bases
Journal of Experimental Algorithmics (JEA)
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We consider the problem of computing a minimum cycle basis of a directed graph with m arcs and n nodes. We adapt the greedy approach proposed by Horton [A polynomial-time algorithm to find the shortest cycle basis of a graph, SIAM J. Comput. 16 (1987) 358] and hereby obtain a very simple exact algorithm of complexity Õ(m4n), being as fast as the first algorithm proposed for this problem [A polynomial time algorithm for minimum cycle basis in directed graphs, Kurt Mehlhorn's List of Publications, 185, MPI, Saarbrücken, 2004, http://www.mpi-sb.mpg.de/∼mehlhorn/ftp/DirCycleBasis.ps; Proc. STACS 2005, submitted for publication]. Moreover, the speed-up of Golynski and Horton [A polynomial time algorithm to find the minimum cycle basis of a regular matroid, in: M. Penttonen, E. Meineche Schmidt (Eds.), SWAT 2002, Lecture Notes in Comput. Sci., vol. 2368, Springer, Berlin, 2002, pp. 200-209] applies to this problem, providing an exact algorithm of complexity Õ(mω+1n), in particular Õ(m3.376n). Finally, we prove that these greedy approaches fail for more specialized subclasses of directed cycle bases.