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A fast algorithm for the generalized parametric minimum cut problem and applications

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Abstract

Many combinatorial optimization problems are solved by a sequence of network flow computations on a network whose edge capacities are given as a function of a parameter λ. Recently Galloet al. [7] made a major advance in solving such parametric flow problems. They showed that for an important class of networks, calledmonotone parametric flow networks, a sequence ofO(n) flow computations could be solved in the same worst-case time bound as a single flow. However, these results require one of two special assumptions: either that the λ values are presented in increasing or decreasing order; or that the edge capacity functions are affine functions of λ. In this paper we show how to remove both of these assumptions while obtaining the same running times as in [7]. This observation generalizes and unifies the two major results of [7], and allows its ideas to be applied to many new combinatorial problems. Of greatest importance, it allows the efficient application of binary search and successive binary search to a sequence of network flow problems.

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Authors and Affiliations

  1. Computer Science Division, University of California, 95616, Davis, CA, USA

    Dan Gusfield & Charles Martel

Authors
  1. Dan Gusfield
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  2. Charles Martel
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Additional information

Communicated by Greg N. Frederickson.

This research was partially supported by Grants CCR-8803704 and CCR-8722848 from the National Science Foundation.

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Gusfield, D., Martel, C. A fast algorithm for the generalized parametric minimum cut problem and applications. Algorithmica 7, 499–519 (1992). https://doi.org/10.1007/BF01758775

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  • DOI: https://doi.org/10.1007/BF01758775

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