A bound for the number of different basic solutions generated by the simplex method

Tomonari Kitahara, Shinji Mizuno

研究成果: Contribution to journalArticle査読

22 被引用数 (Scopus)

抄録

In this short paper, we give an upper bound for the number of different basic feasible solutions generated by the simplex method for linear programming problems (LP) having optimal solutions. The bound is polynomial of the number of constraints, the number of variables, and the ratio between the minimum and the maximum values of all the positive elements of primal basic feasible solutions. When the problem is primal nondegenerate, it becomes a bound for the number of iterations. The result includes strong polynomiality for Markov Decision Problem by Ye (http://www.stanford.edu/∼;:yyye/simplexmdp1.pdf, 2010) and utilize its analysis. We also apply our result to an LP whose constraint matrix is totally unimodular and a constant vector b of constraints is integral.

本文言語英語
ページ(範囲)579-586
ページ数8
ジャーナルMathematical Programming
137
1-2
DOI
出版ステータス出版済み - 2 2013
外部発表はい

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

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