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The Maximum Integer Multiterminal Flow Problem

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Computational Science and Its Applications - ICCSA 2006 (ICCSA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3982))

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Abstract

Given an edge-capacitated graph and kterminal vertices, the maximum integer multiterminal flow problem (MaxIMTF) is to route the maximum number of flow units between the terminals. For directed graphs, we introduce a new parameter k L ≤ k and prove that MaxIMTF is \(\mathcal{NP}\)-hard when k = k L = 2 and when k L = 1 and k = 3, and polynomial-time solvable when k L = 0 and when k L = 1 and k = 2. We also give an 2 log2 (k L + 2)-approximation algorithm for the general case. For undirected graphs, we give a family of valid inequalities for MaxIMTF that has several interesting consequences, and show a correspondence with valid inequalities known for MaxIMTF and for the associated minimum multiterminal cut problem.

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Authors and Affiliations

  1. CEDRIC-CNAM, 292, Rue Saint-Martin, 75141, Paris Cedex 03, France

    Cédric Bentz

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  1. Cédric Bentz
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Editors and Affiliations

  1. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina Gavrilova

  2. Department of Mathematics and Computer Science, University of Perugia, via Vanvitelli, 1, I-06123, Perugia, Italy

    Osvaldo Gervasi

  3. William Norris Professor, Head of the Computer Science and Engineering Department, University of Minnesota, USA

    Vipin Kumar

  4. OptimaNumerics Ltd., Cathedral House, 23-31 Waring Street, BT1 2DX, Belfast, UK

    C. J. Kenneth Tan

  5. Clayton School of IT, Monash University, 3800, Clayton, Australia

    David Taniar

  6. Department of Chemistry, University of Perugia, Via Elce di Sotto, 8, I-06123, Perugia, Italy

    Antonio Laganá

  7. School of Computing, Soongsil University, Seoul, Korea

    Youngsong Mun

  8. School of Information and Communication Engineering, Sungkyunkwan University, Korea

    Hyunseung Choo

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© 2006 Springer-Verlag Berlin Heidelberg

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Bentz, C. (2006). The Maximum Integer Multiterminal Flow Problem. In: Gavrilova, M., et al. Computational Science and Its Applications - ICCSA 2006. ICCSA 2006. Lecture Notes in Computer Science, vol 3982. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11751595_78

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  • DOI: https://doi.org/10.1007/11751595_78

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34075-1

  • Online ISBN: 978-3-540-34076-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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