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Linear programming — Randomization and abstract frameworks

  • Bernd Gärtner
  • Emo Welzl
Invited Lecture
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1046)

Abstract

Recent years have brought some progress in the knowledge of the complexity of linear programming in the unit cost model, and the best result known at this point is a randomized ‘combinatorial’ algorithm which solves a linear program over d variables and n constraints with expected O(d2n+eO(√d log d)) arithmetic operations. The bound relies on two algorithms by Clarkson, and the subexponential algorithms due to Kalai, and to Matoušek, Sharir & Welzl.

We review some of the recent algorithms with their analyses. We also present abstract frameworks like LP-type problems and abstract optimization problems (due to Gärtner) which allow the application of these algorithms to a number of non-linear optimization problems (like polytope distance and smallest enclosing ball of points).

Keywords

Arithmetic Operation Recursive Call Combinatorial Dimension Abstract Framework Primitive Operation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Bernd Gärtner
    • 1
  • Emo Welzl
    • 1
  1. 1.Institut für InformatikFreie Universität BerlinBerlinGermany

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