The Random Edge Simplex Algorithm on Dual Cyclic 4-Polytopes
Combinatorics
2007-05-23 v1 Optimization and Control
Abstract
The simplex algorithm using the random edge pivot-rule on any realization of a dual cyclic 4-polytope with n facets does not take more than O(n) pivot-steps. This even holds for general abstract objective functions (AOF) / acyclic unique sink orientations (AUSO). The methods can be used to show analogous results for products of two polygons. In contrast, we show that the random facet pivot-rule is slow on dual cyclic 4-polytopes, i.e. there are AUSOs on which random facet takes at least \Omega(n^2) steps.
Cite
@article{arxiv.math/0605117,
title = {The Random Edge Simplex Algorithm on Dual Cyclic 4-Polytopes},
author = {Rafael Gillmann},
journal= {arXiv preprint arXiv:math/0605117},
year = {2007}
}
Comments
31 Pages, 11 figures