-

 

 

 




Optimization Online





 

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

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society