### Abstract

Language | English |
---|---|

Number of pages | 16 |

Volume | 2015 |

Publication status | Published - 1 Sep 2015 |

### Publication series

Name | Operations Research Report |
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Publisher | ELTE |

ISSN (Print) | 1215-5918 |

### Fingerprint

### Keywords

- maximum flow problem
- pivot algorithm
- monotonic build-up simplex algorithm

### Cite this

*Strongly polynomial primal monotonic build-up simplex algorithm for maximal flow problems*. (Operations Research Report).

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*Strongly polynomial primal monotonic build-up simplex algorithm for maximal flow problems*. Operations Research Report, vol. 2015.

**Strongly polynomial primal monotonic build-up simplex algorithm for maximal flow problems.** / Illes, Tibor; Molnár-Szipai, Richárd.

Research output: Book/Report › Other report

TY - BOOK

T1 - Strongly polynomial primal monotonic build-up simplex algorithm for maximal flow problems

AU - Illes, Tibor

AU - Molnár-Szipai, Richárd

PY - 2015/9/1

Y1 - 2015/9/1

N2 - 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 is 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 (MBUSA) starts with a feasible solution, and fixes the dual feasibility one variable 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||A|2 pivots.

AB - 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 is 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 (MBUSA) starts with a feasible solution, and fixes the dual feasibility one variable 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||A|2 pivots.

KW - maximum flow problem

KW - pivot algorithm

KW - monotonic build-up simplex algorithm

UR - http://www.cs.elte.hu/opres/orr/download/ORR_2015_02.pdf

M3 - Other report

VL - 2015

T3 - Operations Research Report

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

ER -