IMPROVED ASYMPTOTIC ANALYSIS OF THE AVERAGE NUMBER OF STEPS PERFORMED BY THE SELF-DUAL SIMPLEX ALGORITHM (1986)
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BibTeX
@MISC{Megiddo86improvedasymptotic,
author = {Nimrod Megiddo},
title = { IMPROVED ASYMPTOTIC ANALYSIS OF THE AVERAGE NUMBER OF STEPS PERFORMED BY THE SELF-DUAL SIMPLEX ALGORITHM},
year = {1986}
}
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Abstract
In this paper we analyze the average number of steps performed by the self-dual simplex algorithm for linear programming, under the probabilistic model of spherical symmetry. The model was proposed by Smale. Consider a problem of n variables with m constraints. Smale established that for every number of constraints m, there is a constant c(m) such that the number of pivot steps of the self-dual algorithm, p(m, n), is less than c(m)(ln n)"""'+". We improve upon this estimate by showing that p(m, n) is bounded by a function of m only. The symmetry of the function in m and n implies that p(m, n) is in fact bounded by a function of the smaller of m and n.
