Finding minimum-cost circulations by canceling negative cycles

  • Authors:

  • Andrew Goldberg;Robert Tarjan

  • Affiliations:

  • Department of Computer Science, Stanford University, Stanford, CA;Department of Computer Science, Princeton University, Princeton, New Jersey and AT&T Bell Laboratories, Murray Hill, New Jersey

  • Venue:
  • STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
  • Year:
  • 1988

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Abstract

A classical algorithm for finding a minimum-cost circulation consists of repeatedly finding a residual cycle of negative cost and canceling it by pushing enough flow around the cycle to saturate an arc. We show that a judicious choice of cycles for canceling leads to a polynomial bound on the number of iterations in this algorithm. This gives a very simple strongly polynomial algorithm that uses no scaling. A variant of the algorithm that uses dynamic trees runs in O(nm(log n) min{log(nC), mlog n}) time on a network of n vertices, m arcs, and arc costs of maximum absolute value C. This bound is comparable to those of the fastest previously known algorithms.