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On the Number of Solutions Generated by Dantzig's Simplex Method for LP with Bounded Variables

Tomonari Kitahara (kitahara.t.ab***at***m.titech.ac.jp)
Tomomi Matsui (matsui***at***ise.chuo-u.ac.jp)
Shinji Mizuno (mizuno.s.ab***at***m.titech.ac.jp)

Abstract: We give an upper bound for the number of different basic feasible solutions generated by Dantzig’s simplex method (the simplex method with the most negative pivoting rule) for LP with bounded variables by extending the result of Kitahara and Mizuno (2010). We refine the analysis by them and improve an upper bound for a standard form of LP. Then we utilize the improved bound for an LP with bounded variables. We show some results when the bound is applied to the minimum cost flow problem and the maximum flow problem.

Keywords: Simplex method, Linear programming, Basic feasible solutions, Bounded variables, Minimum cost flow problem, Maximum flow problem.

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

Citation: To appear in Pacific Journal of Optimization.

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Entry Submitted: 02/06/2011
Entry Accepted: 02/06/2011
Entry Last Modified: 02/15/2012

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