A Scaling Algorithm for the Maximum Node-Capacitated Multiflow Problem

Authors:
Maxim A. Babenko;Alexander V. Karzanov
Affiliations:
Dept. of Mechanics and Mathematics, Moscow State University Leninskie Gory, Moscow, Russia 119991;Institute for System Analysis, Moscow, Russia 117312
Venue:
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Year:
2008

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Abstract

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(茂戮驴(n,m,U) n2log2nlogU), where n, m, Uare the number of nodes, the number of edges, and the maximum node capacity, respectively, and 茂戮驴(n,m,U) denotes the complexity of finding a maximum integer flow in a digraph with nnodes, medges, and integer arc capacities not exceeding U茂戮驴茂戮驴+.