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

Authors:
Ravindra K. Ahuja;James B. Orlin
Affiliations:
Department of Industrial & Management Engineering, Indian Institute of Technology, Kanpur 208 016, India;Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Venue:
Operations Research Letters
Year:
1997

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Abstract

In this paper, we study the primal and dual simplex algorithms for the maximum flow problem. We show that any primal simplex algorithm for the maximum flow problem can be converted into a dual simplex algorithm that performs the same number of pivots and runs in the same time. The converse result is also true though in a somewhat weaker form.