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Balancing Applied to Maximum Network Flow Problems

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Algorithms – ESA 2006 (ESA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4168))

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Abstract

We explore balancing as a definitional and algorithmic tool for finding minimum cuts and maximum flows in ordinary and parametric networks. We show that a standard monotonic parametric maximum flow problem can be formulated as a problem of computing a particular maximum flow that is balanced in an appropriate sense. We present a divide-and-conquer algorithm to compute such a balanced flow in a logarithmic number of ordinary maximum-flow computations. For the special case of a bipartite network, we present two simple, local algorithms for computing a balanced flow. The local balancing idea becomes even simpler when applied to the ordinary maximum flow problem. For this problem, we present a round-robin arc-balancing algorithm that computes a maximum flow on an n-vertex, m-arc network with integer arc capacities of at most U in O(n 2 m log(nU)) time. Although this algorithm is slower by at least a factor of n than other known algorithms, it is extremely simple and well-suited to parallel and distributed implementation.

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Author information

Authors and Affiliations

  1. Hewlett-Packard Laboratories, 1501 Page Mill Rd, Palo Alto, CA, 94304, USA

    Robert Tarjan, Julie Ward, Bin Zhang, Yunhong Zhou & Jia Mao

Authors
  1. Robert Tarjan
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  2. Julie Ward
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  3. Bin Zhang
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  4. Yunhong Zhou
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  5. Jia Mao
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Editor information

Editors and Affiliations

  1. Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA and School of Computer Science, Tel-Aviv University, 69978, Tel-Aviv, Israel

    Yossi Azar

  2. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Thomas Erlebach

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© 2006 Springer-Verlag Berlin Heidelberg

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Tarjan, R., Ward, J., Zhang, B., Zhou, Y., Mao, J. (2006). Balancing Applied to Maximum Network Flow Problems. In: Azar, Y., Erlebach, T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841036_55

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  • DOI: https://doi.org/10.1007/11841036_55

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-38875-3

  • Online ISBN: 978-3-540-38876-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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