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
Graph Theory with Applications to Engineering and Computer Science (Prentice Hall Series in Automatic Computation)
Algorithms to Compute Minimum Cycle Basis in Directed Graphs
Theory of Computing Systems
A greedy approach to compute a minimum cycle basis of a directed graph
Information Processing Letters
An Õ(m2n) randomized algorithm to compute a minimum cycle basis of a directed graph
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On a Special Co-cycle Basis of Graphs
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
An improved heuristic for computing short integral cycle bases
Journal of Experimental Algorithmics (JEA)
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
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 in a directed graph. The input to this problem is a directed graph G whose edges have non-negative weights. A cycle in this graph is actually a cycle in the underlying undirected graph with edges traversable in both directions. A {–1,0,1} edge incidence vector is associated with each cycle: edges traversed by the cycle in the right direction get 1 and edges traversed in the opposite direction get -1. The vector space over ℚ generated by these vectors is the cycle space of G. A minimum cycle basis is a set of cycles of minimum weight that span the cycle space of G. The current fastest algorithm for computing a minimum cycle basis in a directed graph with m edges and n vertices runs in $\tilde{O}(m^{\omega+1}n)$ time (where ωO(m3n + m2n2logn) algorithm. We also slightly improve the running time of the current fastest randomized algorithm from O(m2nlogn) to O(m2n + mn2 logn).