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Random walks, totally unimodular matrices, and a randomised dual simplex algorithm

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Abstract

We discuss the application of random walks to generating a random basis of a totally unimodular matrix and to solving a linear program with such a constraint matrix. We also derive polynomial upper bounds on the combinatorial diameter of an associated polyhedron.

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Authors and Affiliations

  1. School of Computer Studies, University of Leeds, LS2 9JT, Leeds, UK

    Martin Dyer

  2. Department of Mathematics, Carnegie-Mellon University, 15213-3890, Pittsburgh, PA, USA

    Alan Frieze

Authors
  1. Martin Dyer
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  2. Alan Frieze
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Additional information

Supported by NATO grant RG0088/89.

Corresponding author. Supported by NSF grants CCR-8900112, CCR-9024935 and NATO grant RG0088/89.

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Dyer, M., Frieze, A. Random walks, totally unimodular matrices, and a randomised dual simplex algorithm. Mathematical Programming 64, 1–16 (1994). https://doi.org/10.1007/BF01582563

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  • DOI: https://doi.org/10.1007/BF01582563

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