Random Walks on Polytopes of Constant Corank

Author Malte Milatz



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Malte Milatz

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Malte Milatz. Random Walks on Polytopes of Constant Corank. In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 60:1-60:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.SoCG.2018.60

Abstract

We show that the pivoting process associated with one line and n points in r-dimensional space may need Omega(log^r n) steps in expectation as n -> infty. The only cases for which the bound was known previously were for r <= 3. Our lower bound is also valid for the expected number of pivoting steps in the following applications: (1) The Random-Edge simplex algorithm on linear programs with n constraints in d = n-r variables; and (2) the directed random walk on a grid polytope of corank r with n facets.
Keywords
  • polytope
  • unique sink orientation
  • grid
  • random walk

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