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A Proof by the Simplex Method for the Diameter of a (0,1)-Polytope

Tomonari Kitahara(kitahara.t.ab***at***m.titech.ac.jp)
Shinji Mizuno(mizuno.s.ab***at***m.titech.ac.jp)

Abstract: Naddef shows that the Hirsch conjecture is true for (0,1)-polytopes by proving that the diameter of any $(0,1)$-polytope in $d$-dimensional Euclidean space is at most $d$. In this short paper, we give a simple proof for the diameter. The proof is based on the number of solutions generated by the simplex method for a linear programming problem. Our work is motivated by Kitahara and Mizuno, in which they get upper bounds for the number of different solutions generated by the simplex method.

Keywords: (0,1)-polytope, Diameter, Hirsh conjecture, Linear programming, Simplex method

Category 1: Linear, Cone and Semidefinite Programming (Linear Programming )

Category 2: Combinatorial Optimization (Graphs and Matroids )

Citation: Technical paper, Tokyo Institute of Technology

Download: [PDF]

Entry Submitted: 08/24/2011
Entry Accepted: 08/24/2011
Entry Last Modified: 08/24/2011

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