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A Scaling Algorithm for the Maximum Node-Capacitated Multiflow Problem

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Algorithms - ESA 2008 (ESA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5193))

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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(Λ(n,m,U) n 2 log2 n logU), 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 arc capacities not exceeding U ∈ ℤ + .

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Author information

Authors and Affiliations

  1. Dept. of Mechanics and Mathematics, Moscow State University Leninskie Gory, 119991, Moscow, Russia

    Maxim A. Babenko

  2. Institute for System Analysis, 9, Prospect 60 Let Oktyabrya, 117312, Moscow, Russia

    Alexander V. Karzanov

Authors
  1. Maxim A. Babenko
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  2. Alexander V. Karzanov
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Dan Halperin Kurt Mehlhorn

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© 2008 Springer-Verlag Berlin Heidelberg

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Babenko, M.A., Karzanov, A.V. (2008). A Scaling Algorithm for the Maximum Node-Capacitated Multiflow Problem. In: Halperin, D., Mehlhorn, K. (eds) Algorithms - ESA 2008. ESA 2008. Lecture Notes in Computer Science, vol 5193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87744-8_11

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  • DOI: https://doi.org/10.1007/978-3-540-87744-8_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87743-1

  • Online ISBN: 978-3-540-87744-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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