Combinatorial Linear Programming: Geometry Can Help

  • Bernd Gärtner
Conference paper
Part of the Lecture Notes in Computer Science book series (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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Bernd Gärtner
    • 1
  1. 1.Institut für Theoretische InformatikETH Zürich, ETH-ZentrumZürichSwitzerland

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