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 - https://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 -