Strongly polynomial primal monotonic build-up simplex algorithm for maximal flow problems

Tibor Illés, Molnár-Szipai Richárd

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The maximum flow problem (MFP) is a fundamental model in operations research. The network simplex algorithm is one of the most efficient solution methods for MFP in practice. The theoretical properties of established pivot algorithms for MFP are less understood. Variants of the primal simplex and dual simplex methods for MFP have been proven strongly polynomial, but no similar result exists for other pivot algorithms like the monotonic build-up or the criss-cross simplex algorithm.

The monotonic build-up simplex algorithm (MBU SA) starts with a feasible solution, and fixes the dual feasibility one variable at a time, temporarily losing primal feasibility. In the case of maximum flow problems, pivots in one such iteration are all dual degenerate, bar the last one. Using a labelling technique to break these ties we show a variant that solves the maximum flow problem in 2|V||E|2 pivots.
Original languageEnglish
Pages (from-to)201-210
Number of pages10
JournalDiscrete Applied Mathematics
Early online date22 Jul 2016
Publication statusPublished - 11 Dec 2016


  • maximum flow problem
  • pivot algorithms
  • MBU algorithm
  • operations research
  • polynomial
  • simplex algorithms
  • labelling technique


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