Islamic Azad University, Rasht BranchIranian Journal of Optimization2588-57236120100901Linear Programming, the Simplex Algorithm and Simple PolytopesLinear Programming, the Simplex Algorithm and Simple Polytopes702719514145ENDas SashiBhusanDepartment of Mathematics,Balasor college of Engg & Teach. Sergarh, Balasore, Orissa, IndiaBiswalBagabanDepartment of Mathematics F.M.Autonomous College, Balasore, Orissa, IndiaJ.PTripathyDepartment of Mathematics Gurukul Institute of Bhubaneswar,Orissa,IndiaJournal Article20100730<span>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. </span>http://ijo.iaurasht.ac.ir/article_514145_14206dbab009fd1cc3c9f07538d444cf.pdf