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

Author

Listed:
  • Shmuel Onn

    (Technion—Israel Institute of Technology)

  • Uriel G. Rothblum

    (Technion—Israel Institute of Technology)

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.

Suggested Citation

  • Shmuel Onn & Uriel G. Rothblum, 2007. "The use of edge-directions and linear programming to enumerate vertices," Journal of Combinatorial Optimization, Springer, vol. 14(2), pages 153-164, October.
    • Handle: RePEc:spr:jcomop:v:14:y:2007:i:2:d:10.1007_s10878-007-9063-7
    DOI: 10.1007/s10878-007-9063-7
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    References listed on IDEAS

    as
    1. Shmuel Onn & Leonard J. Schulman, 2001. "The Vector Partition Problem for Convex Objective Functions," Mathematics of Operations Research, INFORMS, vol. 26(3), pages 583-590, August.
    2. Frank K. Hwang & Uriel G. Rothblum, 1996. "Directional-Quasi-Convexity, Asymmetric Schur-Convexity and Optimality of Consecutive Partitions," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 540-554, August.
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