A new approach to the maximum-flow problem
Journal of the ACM (JACM)
A data structure for dynamic trees
Journal of Computer and System Sciences
Maximum skew-symmetric flows and matchings
Mathematical Programming: Series A and B
Acyclic bidirected and skew-symmetric graphs: algorithms and structure
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Minimum mean cycle problem in bidirected and skew-symmetric graphs
Discrete Optimization
Min-cost multiflows in node-capacitated undirected networks
Journal of Combinatorial Optimization
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A graph (digraph) G=(V,E) with a set T@?V of terminals is called inner Eulerian if each nonterminal node v has even degree (resp. the numbers of edges entering and leaving v are equal). Cherkassky and Lovasz, independently, showed that the maximum number of pairwise edge-disjoint T-paths in an inner Eulerian graph G is equal to 12@?"s"@?"T@l(s), where @l(s) is the minimum number of edges whose removal disconnects s and T-{s}. A similar relation for inner Eulerian digraphs was established by Lomonosov. Considering undirected and directed networks with ''inner Eulerian'' edge capacities, Ibaraki, Karzanov, and Nagamochi showed that the problem of finding a maximum integer multiflow (where partial flows connect arbitrary pairs of distinct terminals) is reduced to O(logT) maximum flow computations and to a number of flow decompositions. In this paper we extend the above max-min relation to inner Eulerian bidirected graphs and inner Eulerian skew-symmetric graphs and develop an algorithm of complexity O(VElogTlog(2+V^2/E)) for the corresponding capacitated cases. In particular, this improves the best known bound for digraphs. Our algorithm uses a fast procedure for decomposing a flow with O(1) sources and sinks in a digraph into the sum of one-source-one-sink flows.