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Publication
Bulletin of the American Mathematical Society
Paper
New results on the average behavior of simplex algorithms
Abstract
It has been a challenge for mathematicians to theoretically confirm the extremely good performance of simplex algorithms for linear programming. We have confirmed that a certain variant of the simplex method solves problems of order m × n in an expected number of steps which is bounded between two quadratic functions of the smaller dimension of the problem. Our probabilistic assumptions are rather weak. © 1984 American Mathematical Society.