Mathematical Programming

, Volume 50, Issue 1–3, pp 277–290 | Cite as

Use of dynamic trees in a network simplex algorithm for the maximum flow problem

  • Andrew V. Goldberg
  • Michael D. Grigoriadis
  • Robert E. Tarjan
Article

Abstract

Goldfarb and Hao (1990) have proposed a pivot rule for the primal network simplex algorithm that will solve a maximum flow problem on ann-vertex,m-arc network in at mostnm pivots and O(n2m) time. In this paper we describe how to extend the dynamic tree data structure of Sleator and Tarjan (1983, 1985) to reduce the running time of this algorithm to O(nm logn). This bound is less than a logarithmic factor larger than those of the fastest known algorithms for the problem. Our extension of dynamic trees is interesting in its own right and may well have additional applications.

Key words

Algorithms complexity data structures dynamic trees graphs linear programming maximum flow network flow network optimization 

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Copyright information

© The Mathematical Programming Society, Inc. 1991

Authors and Affiliations

  • Andrew V. Goldberg
    • 1
  • Michael D. Grigoriadis
    • 2
  • Robert E. Tarjan
    • 3
    • 4
  1. 1.Department of Computer ScienceStanford UniversityStanfordUSA
  2. 2.Department of Computer ScienceRutgers UniversityNew BrunswickUSA
  3. 3.Department of Computer SciencePrinceton UniversityPrincetonUSA
  4. 4.AT&T Bell LaboratoriesMurray HillUSA

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