The null space problem I. complexity
SIAM Journal on Algebraic and Discrete Methods
Matrix multiplication via arithmetic progressions
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
A polynomial-time algorithm to find the shortest cycle basis of a graph
SIAM Journal on Computing
Beyond the flow decomposition barrier
Journal of the ACM (JACM)
A greedy approach to compute a minimum cycle basis of a directed graph
Information Processing Letters
Implementing minimum cycle basis algorithms
Journal of Experimental Algorithmics (JEA)
Discrete Applied Mathematics
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)
Minimum Cycle Bases and Their Applications
Algorithmics of Large and Complex Networks
Minimum cycle bases: Faster and simpler
ACM Transactions on Algorithms (TALG)
Minimum Cycle Bases of Weighted Outerplanar Graphs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Finding good cycle constraints for large scale multi-robot SLAM
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
A greedy approach to compute a minimum cycle basis of a directed graph
Information Processing Letters
Minimum cut bases in undirected networks
Discrete Applied Mathematics
New approximation algorithms for minimum cycle bases of graphs
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Minimum cycle bases of weighted outerplanar graphs
Information Processing Letters
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
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
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
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
Implementing minimum cycle basis algorithms
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
Efficient deterministic algorithms for finding a minimum cycle basis in undirected graphs
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Survey: Cycle bases in graphs characterization, algorithms, complexity, and applications
Computer Science Review
Integral cycle bases for cyclic timetabling
Discrete Optimization
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An algorithm is given to solve the minimum cycle basis problem for regular matroids. The result is based upon Seymour's decomposition theorem for regular matroids; the Gomory-Hu tree, which is essentially the solution for cographic matroids; and the corresponding result for graphs. The complexity of the algorithm is O((n + m)4), provided that a regular matroid is represented as a binary n脳m matrix. The complexity decreases to O((n+m)3.376) using fast matrix multiplication.