A polynomial-time algorithm to find the shortest cycle basis of a graph
SIAM Journal on Computing
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
The All-Pairs Min Cut Problem and the Minimum Cycle Basis Problem on Planar Graphs
SIAM Journal on Discrete Mathematics
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
A 2-Approximation Algorithm for the Undirected Feedback Vertex Set Problem
SIAM Journal on Discrete Mathematics
Solving the feedback vertex set problem on undirected graphs
Discrete Applied Mathematics
Algorithms for Generating Fundamental Cycles in a Graph
ACM Transactions on Mathematical Software (TOMS)
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
Implementing minimum cycle basis algorithms
Journal of Experimental Algorithmics (JEA)
Discrete Applied Mathematics
Minimum cycle bases: Faster and simpler
ACM Transactions on Algorithms (TALG)
Survey: Cycle bases in graphs characterization, algorithms, complexity, and applications
Computer Science Review
Properties of Gomory-Hu co-cycle bases
Theoretical Computer Science
Testing connectivity of faulty networks in sublinear time
Journal of Discrete Algorithms
Hi-index | 0.00 |
We consider the problem of, given an undirected graph G with a nonnegative weight on each edge, finding a basis of the cycle space of G of minimum total weight, where the total weight of a basis is the sum of the weights of its cycles. Minimum cycle bases are of interest in a variety of fields. In [13] Horton proposed a first polynomial-time algorithm where a minimum cycle basis is extracted from a polynomial-size subset of candidate cycles in O(m3n) by using Gaussian elimination. In a different approach, due to de Pina [7] and refined in [15], the cycles of a minimum cycle basis are determined sequentially in O(m2n+mn2 logn). A more sophisticated hybrid algorithm proposed in [18] has the best worst-case complexity of O(m2n / logn+mn2). In this work we revisit Horton's and de Pina's approaches and we propose a simple hybrid algorithm which improves the worst-case complexity to O(m2n / logn). We also present a very efficient related algorithm that relies on an adaptive independence test à la de Pina. Computational results on a wide set of instances show that the latter algorithm outperforms the previous algorithms by one or two order of magnitude on medium-size instances and allows to solve instances with up to 3000 vertices in a reasonable time.