Linear Programming, the Simplex Algorithm and Simple Polytopes

Subject Areas : linear Programming

Das  Bhusan ¹ (Department of Mathematics,Balasor college of Engg & Teach. Sergarh, Balasore, Orissa, India)
Biswal  Bagaban ² (Department of Mathematics F.M.Autonomous College, Balasore, Orissa, India)
J.P  Tripathy ³ (Department of Mathematics Gurukul Institute of Bhubaneswar,Orissa,India)

Received: 2010-07-30 Accepted : 2010-08-30 Published : 2010-09-01

Keywords: simplex algorithm, Randomized Pivot rule complexity combinational theory of simple polytopes,

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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