An O(VE) algorithm for ear decompositions of matching-covered graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
An O(VE) algorithm for ear decompositions of matching-covered graphs
ACM Transactions on Algorithms (TALG)
Free multiflows in bidirected and skew-symmetric graphs
Discrete Applied Mathematics
Acyclic bidirected and skew-symmetric graphs: algorithms and structure
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
An algorithm for (n-3)-connectivity augmentation problem: Jump system approach
Journal of Combinatorial Theory Series B
Fast matrix rank algorithms and applications
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Minimum mean cycle problem in bidirected and skew-symmetric graphs
Discrete Optimization
A simple reduction from maximum weight matching to maximum cardinality matching
Information Processing Letters
Min-cost multiflows in node-capacitated undirected networks
Journal of Combinatorial Optimization
Fast matrix rank algorithms and applications
Journal of the ACM (JACM)
Linear-Time Approximation for Maximum Weight Matching
Journal of the ACM (JACM)
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The maximum integer skew-symmetric flow problem (MSFP) generalizes both the maximum flow and maximum matching problems. It was introduced by Tutte [28] in terms of self-conjugate flows in antisymmetrical digraphs. He showed that for these objects there are natural analogs of classical theoretical results on usual network flows, such as the flow decomposition, augmenting path, and max-flow min-cut theorems. We give unified and shorter proofs for those theoretical results. We then extend to MSFP the shortest augmenting path method of Edmonds and Karp [7] and the blocking flow method of Dinits [4], obtaining algorithms with similar time bounds in general case. Moreover, in the cases of unit arc capacities and unit “node capacities” our blocking skew-symmetric flow algorithm has time bounds similar to those established in [8, 21] for Dinits’ algorithm. In particular, this implies an algorithm for finding a maximum matching in a nonbipartite graph in * time, which matches the time bound for the algorithm of Micali and Vazirani [25]. Finally, extending a clique compression technique of Feder and Motwani [9] to particular skew-symmetric graphs, we speed up the implied maximum matching algorithm to run in * time, improving the best known bound for dense nonbipartite graphs. Also other theoretical and algorithmic results on skew-symmetric flows and their applications are presented.