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The Random Edge Simplex Algorithm on Dual Cyclic 4-Polytopes

Rafael Gillmann
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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 Ω(n^2) steps.

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Rafael Gillmann. 2006-05-04. The Random Edge Simplex Algorithm on Dual Cyclic 4-Polytopes. https://arxiv.org/abs/math/0605117

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