Linear programming, the simplex algorithm and simple polytopes

In the first part of the paper we survey some far-reaching applications of the basic facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concerning the simplex algorithm. We describe subexponential randomized pivot rules and upper bounds on the diameter of graphs of polytopes. © 1997 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.

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