Linear Programming, the Simplex Algorithm and Simple Polytopes

Iranian Journal of Optimization

مقاله 3، دوره 6، شماره 1، فروردین 2014، صفحه 702-719   

نوع مقاله: Research Paper

نویسندگان

Das Sashi Bhusan¹؛ Biswal Bagaban²؛ J.P Tripathy^{* 3}

¹Department of Mathematics,Balasor college of Engg & Teach. Sergarh, Balasore, Orissa, India

²Department of Mathematics F.M.Autonomous College, Balasore, Orissa, India

³Department of Mathematics Gurukul Institute of Bhubaneswar,Orissa,India

چکیده

In the first part of the paper we survey some far reaching applications of the basis facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concurring the simplex algorithm. We describe sub-exponential randomized pivot roles and upper bounds on the diameter of graphs of polytopes. 

کلیدواژه‌ها

simplex algorithm؛ Randomized Pivot rule complexity combinational theory of simple polytopes

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