License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2018.60
URN: urn:nbn:de:0030-drops-87730
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8773/
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Milatz, Malte

Random Walks on Polytopes of Constant Corank

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LIPIcs-SoCG-2018-60.pdf (0.6 MB)

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.

BibTeX - Entry

@InProceedings{milatz:LIPIcs:2018:8773,
  author =	{Malte Milatz},
  title =	{{Random Walks on Polytopes of Constant Corank}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{60:1--60:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Bettina Speckmann and Csaba D. T{\'o}th},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8773},
  URN =		{urn:nbn:de:0030-drops-87730},
  doi =		{10.4230/LIPIcs.SoCG.2018.60},
  annote =	{Keywords: polytope, unique sink orientation, grid, random walk}
}

Keywords: polytope, unique sink orientation, grid, random walk
Collection: 34th International Symposium on Computational Geometry (SoCG 2018)
Issue Date: 2018
Date of publication: 08.06.2018

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