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Journal of Combinatorial Optimization

, Volume 14, Issue 2–3, pp 153–164 | Cite as

The use of edge-directions and linear programming to enumerate vertices

  • Shmuel OnnEmail author
  • Uriel G. Rothblum
Article

Abstract

Given a list of vectors that contains directions of the edges of a given polytope ℘ and the availability of an algorithm that solves linear programs over ℘, we describe a method for enumerating the vertices of ℘; in particular, the method is adaptable to polytopes which are presented as (linear) projections of polytopes having linear inequality representation. Polynomial complexity bounds under both the real and the binary computation models are derived when the dimension of the polytope is fixed and the given LP algorithm is polynomial.

Keywords

Vertices Polytopes Edge-directions Linear programming 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Technion—Israel Institute of TechnologyHaifaIsrael

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