Bhusan, D., Bagaban, B., Tripathy, J. (2010). Linear Programming, the Simplex Algorithm and Simple Polytopes. Iranian Journal of Optimization, 6(1), 567-590.

Das Sashi Bhusan; Biswal Bagaban; J.P Tripathy. "Linear Programming, the Simplex Algorithm and Simple Polytopes". Iranian Journal of Optimization, 6, 1, 2010, 567-590.

Bhusan, D., Bagaban, B., Tripathy, J. (2010). 'Linear Programming, the Simplex Algorithm and Simple Polytopes', Iranian Journal of Optimization, 6(1), pp. 567-590.

Bhusan, D., Bagaban, B., Tripathy, J. Linear Programming, the Simplex Algorithm and Simple Polytopes. Iranian Journal of Optimization, 2010; 6(1): 567-590.

Linear Programming, the Simplex Algorithm and Simple Polytopes

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

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

^{3}Department of Mathematics Gurukul Institute of Bhubaneswar,Orissa,India

Receive Date: 30 July 2010,
Revise Date: 30 August 2010,
Accept Date: 30 August 2010

Abstract

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.

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