New results on the average behavior of simplex algorithms

Ilan Adler, Nimrod Megiddo, Michael J. Todd
1984 Bulletin of the American Mathematical Society  
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 X 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.
doi:10.1090/s0273-0979-1984-15317-5 fatcat:dwof6kmkevcoxp6xe2uboimjxi