Balancing applied to maximum network flow problems

  • Authors:

  • Robert Tarjan;Julie Ward;Bin Zhang;Yunhong Zhou;Jia Mao

  • Affiliations:

  • Hewlett-Packard Laboratories, Palo Alto, CA;Hewlett-Packard Laboratories, Palo Alto, CA;Hewlett-Packard Laboratories, Palo Alto, CA;Hewlett-Packard Laboratories, Palo Alto, CA;Hewlett-Packard Laboratories, Palo Alto, CA

  • Venue:
  • ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
  • Year:
  • 2006

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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(n2m 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.