The use of edge-directions and linear programming to enumerate vertices
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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.
KeywordsVertices Polytopes Edge-directions Linear programming
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- Cook WJ, Cunningham WH, Pulleyblank WR, Schrijver A (1997) Combinatorial optimization. Wiley, New York Google Scholar
- Harding EF (1967) The number of partitions of a set of n points in k dimensions induced by hyperplanes. In: Proceedings of the Edinburgh mathematical society, vol 15, pp 285–289 Google Scholar
- Rockaffelar RT (1984) Network flows and monotropic optimization. Pure and applied mathematics. Wiley–Interscience, New York Google Scholar
- Schulz AS, Weismantel R, Ziegler G (1995) (0,1)-integer programming: optimization and augmentation are equivalent. In: Proceedings of the third annual European symposium on algorithms. Lecture notes in computer science, vol 979. Springer, Berlin, pp 473–483 Google Scholar
- Zaslavsky T (1975) Facing up to arrangements: face count formulas for partitions of space by hyperplanes. Mem Am Math Soc 154 Google Scholar
- Ziegler GM (1995) Lecture notes on polytopes. Graduate texts in mathematics. Springer, New York Google Scholar