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
On a Special Co-cycle Basis of Graphs
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Minimum Cycle Bases and Their Applications
Algorithmics of Large and Complex Networks
Minimum cycle bases: Faster and simpler
ACM Transactions on Algorithms (TALG)
New approximation algorithms for minimum cycle bases of graphs
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Properties of Gomory-Hu co-cycle bases
Theoretical Computer Science
A faster deterministic algorithm for minimum cycle bases in directed graphs
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Survey: Cycle bases in graphs characterization, algorithms, complexity, and applications
Computer Science Review
Integral cycle bases for cyclic timetabling
Discrete Optimization
Minimum cycle bases in graphs algorithms and applications
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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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 O@?(m^4n), 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, Saarbrucken, 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 O@?(m^@w^+^1n), in particular O@?(m^3^.^3^7^6n). Finally, we prove that these greedy approaches fail for more specialized subclasses of directed cycle bases.