On strongly polynomial variants of the network simplex algorithm for the maximum flow problem

Authors:
Donald Goldfarb;Jianxiu Hao
Affiliations:
Department of Industrial Engineering and Operations Research, Columbia University, New York 10027, USA;GTE Laboratories, 40 Sylvan Road, Waltham, MA 02254, USA
Venue:
Operations Research Letters
Year:
1991

Citing 4
Cited 1

Fast algorithms for bipartite network flow

SIAM Journal on Computing
A primal simplex algorithm that solves the maximum flow problem in at most nm pivots and o(n2m) time

Mathematical Programming: Series A and B
Use of dynamic trees in a network simplex algorithm for the maximum flow problem

Mathematical Programming: Series A and B
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems

Journal of the ACM (JACM)

Equivalence of the primal and dual simplex algorithms for the maximum flow problem

Operations Research Letters

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Abstract

We give a short proof that the network simplex algorithm with either the smaller label or the smallest label pivot rules proposed by D. Goldfarb and J. Hao, solves a maximum flow problem on an n-node, m-arc network in at most nm pivots and O(n^2m) time. We also show that a straightforward adaptation of a shortest augmenting path algorithm is not polynomial.