An O(VE) algorithm for ear decompositions of matching-covered graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Fast sparse matrix multiplication
ACM Transactions on Algorithms (TALG)
An O(VE) algorithm for ear decompositions of matching-covered graphs
ACM Transactions on Algorithms (TALG)
Finding all maximally-matchable edges in a bipartite graph
Theoretical Computer Science
Efficient algorithms for weighted rank-maximal matchings and related problems
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Fast matrix rank algorithms and applications
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Fast matrix rank algorithms and applications
Journal of the ACM (JACM)
| Hi-index | 0.00 |
A randomized (Las Vegas) algorithm is given for finding the Gallai--Edmonds decomposition of a graph. Let n denote the number of vertices, and let M(n) denote the number of arithmetic operations for multiplying two n $\times$ n matrices. The sequential running time (i.e., number of bit operations) is within a poly-logarithmic factor of M(n). The parallel complexity is O((log n)2) parallel time using a number of processors within a poly-logarithmic factor of M(n). The same complexity bounds suffice for solving several other problems: finding a minimum vertex cover in a bipartite graph finding a minimum X --- Y vertex separator in a directed graph, where X and Y are specified sets of vertices, finding the allowed edges (i.e., edges that occur in some maximum matching) of a graph, finding the canonical partition of the vertex set of an elementary graph. The sequential algorithms for problems (i), (ii), and (iv) are Las Vegas, and the algorithm for problem (iii) is Monte Carlo. The new complexity bounds are significantly better than the best previous ones, e.g., using the best value of M(n) currently known, the new sequential running time is O(n2.38) versus the previous best O(n2.5 /(log n)) or more.