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International Workshop on Randomization and Approximation Techniques in Computer Science

RANDOM 1998: Randomization and Approximation Techniques in Computer Science pp 82–96Cite as

Combinatorial Linear Programming: Geometry Can Help

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1518))

Abstract

We consider a class A of generalized linear programs on the d-cube (due to Matoušek) and prove that Kalai’s subexponential simplex algorithm Random-Facet is polynomial on all actual linear programs in the class. In contrast, the subexponential analysis is known to be best possible for general instances in A. Thus, we identify a “geometric” property of linear programming that goes beyond all abstract notions previously employed in generalized linear programming frameworks, and that can be exploited by the simplex method in a nontrivial setting.

supported by the Swiss Science Foundation (SNF), project No. 21-50647.97.

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Author information

Authors and Affiliations

  1. Institut für Theoretische Informatik, ETH Zürich, ETH-Zentrum, CH-8092, Zürich, Switzerland

    Bernd Gärtner

Authors
  1. Bernd Gärtner
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Editor information

Editors and Affiliations

  1. International Computer Science Institute, 1947 Center Street, Suite 600, Berkeley, CA, 94704-1198, USA

    Michael Luby

  2. Computer Science Department, University of Geneva, 24, rue Général Dufour, CH-1211, Geneva 4, Switzerland

    José D. P. Rolim

  3. University of Barcelona (UPC), Jordi Girona Salgado 1-3, E-08034, Barcelona, Spain

    Maria Serna

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© 1998 Springer-Verlag Berlin Heidelberg

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Gärtner, B. (1998). Combinatorial Linear Programming: Geometry Can Help. In: Luby, M., Rolim, J.D.P., Serna, M. (eds) Randomization and Approximation Techniques in Computer Science. RANDOM 1998. Lecture Notes in Computer Science, vol 1518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49543-6_8

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  • DOI: https://doi.org/10.1007/3-540-49543-6_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65142-0

  • Online ISBN: 978-3-540-49543-7

  • eBook Packages: Springer Book Archive

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