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Algorithms and complexity analysis for some flow problems

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Abstract

Several network-flow problems with additional constraints are considered. They are all special cases of the linear-programming problem and are shown to be ℘-complete. It is shown that the existence of a strongly polynomial-time algorithm for any of these problems implies the existence of such an algorithm for the general linear-programming problem. On the positive side, strongly polynomial algorithms for some parametric flow problems are given, when the number of parameters is fixed. These algorithms are applicable to constrained flow problems when the number of additional constraints is fixed.

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Author information

Author notes

  1. Edith Cohen

    Present address: Currently at AT&T Bell Laboratories, 600 Mountain Avenue, 07974, Murray Hill, NJ, USA

Authors and Affiliations

  1. IBM Almaden Research Center, 95120-6099, San Jose, CA, USA

    Nimrod Megiddo

  2. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel

    Nimrod Megiddo

Authors
  1. Edith Cohen
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  2. Nimrod Megiddo
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Additional information

Communicated by Harold N. Gabow.

Work on the paper was done while at Stanford University and IBM Almaden Research Center. This research was partially supported by NSF PYI Grant CCR-8858097.

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Cohen, E., Megiddo, N. Algorithms and complexity analysis for some flow problems. Algorithmica 11, 320–340 (1994). https://doi.org/10.1007/BF01240739

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  • DOI: https://doi.org/10.1007/BF01240739

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