The Random Edge Simplex Algorithm on Dual Cyclic 4-Polytopes

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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.
31 Pages, 11 figures

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Combinatorics, Optimization and Control, 90C05 (Primary); 52B12, 68W20 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/112656

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0605117
 http://arxiv.org/abs/math/0605117

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arXiv