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Randomized Simplex Algorithms

  1. Bernd Gärtner

Published Online: 15 SEP 2010

DOI: 10.1002/9780470400531.eorms0706

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Gärtner, B. 2010. Randomized Simplex Algorithms. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. Institute of Theoretical Computer Science ETH, Zurich, Switzerland

Publication History

  1. Published Online: 15 SEP 2010

Abstract

A randomized simplex algorithm is a variant of the simplex method in which the rule for choosing the entering variable is randomized. This means that in each pivot step, the choice of the entering variable may depend in a well-defined way on the outcome of a random experiment. The performance of a randomized simplex algorithm on a given linear program is measured in terms of the expected number of pivot steps taken. Randomized simplex algorithms are studied in the context of the complexity of the simplex method. Randomization allows to beat the known worst-case complexity bounds of deterministic simplex algorithms.

Keywords:

  • randomized simplex algorithm;
  • worst-case analysis;
  • random-edge;
  • random-facet;
  • subexponential;
  • polytope digraphs;
  • Hirsch conjecture;
  • LP-type problems