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

Shmuel Onn () and Uriel G. Rothblum ()
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Shmuel Onn: Technion—Israel Institute of Technology
Uriel G. Rothblum: Technion—Israel Institute of Technology

Journal of Combinatorial Optimization, 2007, vol. 14, issue 2, No 6, 153-164

Abstract: 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 (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10878-007-9063-7

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