On the Variance of the Number of Pivot Steps Required by the Simplex Algorithm

  • Despite their very good empirical performance most of the simplex algorithm's variants require exponentially many pivot steps in terms of the problem dimensions of the given linear programming problem (LPP) in worst-case situtation. The first to explain the large gap between practical experience and the disappointing worst-case was Borgwardt (1982a,b), who could prove polynomiality on tbe average for a certain variant of the algorithm-the " Schatteneckenalgorithmus (shadow vertex algorithm)" - using a stochastic problem simulation.

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Author:Karl-Heinz Küfer
Series (Serial Number):Preprints (rote Reihe) des Fachbereich Mathematik (238)
Document Type:Report
Language of publication:English
Date of Publication (online):2017/10/18
Year of first Publication:1993
Publishing Institution:Technische Universität Kaiserslautern
Date of the Publication (Server):2017/10/18
Page Number:12
Faculties / Organisational entities:Kaiserslautern - Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0)