Algorithmica

, Volume 11, Issue 3, pp 226–242 | Cite as

Tight bounds on the number of minimum-mean cycle cancellations and related results

  • Tomasz Radzik
  • Andrew V. Goldberg
Article

Abstract

We prove a tight Θ(min(nm log(nC), nm2)) bound on the number of iterations of the minimum-mean cycle-canceling algorithm of Goldberg and Tarjan [13]. We do this by giving the lower bound and by improving the strongly polynomial upper bound on the number of iterations toO(nm2). We also give an improved version of the maximum-mean cut canceling algorithm of [7], which is a dual of the minimum-mean cycle-canceling algorithm. Our version of the dual algorithm runs in O(nm2) iterations.

Key words

Network flow problems Minimum cost flow Minimum cost circulation Combinatorial optimization Cycle canceling algorithms Strongly polynomial algorithms 

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Copyright information

© Springer-Verlag New York Inc. 1994

Authors and Affiliations

  • Tomasz Radzik
    • 1
  • Andrew V. Goldberg
    • 1
  1. 1.Computer Science DepartmentStanford UniversityStanfordUSA

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