A Scaling Algorithm for the Maximum Node-Capacitated Multiflow Problem
نویسندگان
چکیده
We study the problem of finding a fractional node-capacitated multiflow of maximum value in an undirected network. Previously known methods for this problem are based on linear programming and the ellipsoid method. In this paper we apply a capacity scaling approach and develop a purely combinatorial weakly polynomial algorithm of time complexity O(Λ(n, m, U) n log n log U), where n, m, U are the number of nodes, the number of edges, and the maximum node capacity, respectively, and Λ(n, m, U) denotes the complexity of finding a maximum integer flow in a digraph with n nodes, m edges, and integer edge capacities not exceeding U ∈ Z+.
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