Who Solved the Hirsch Conjecture ?

However, empirical experience with thousands of practical problems indicates that the number of iterations is usually close to the number of basic variables in the final set which were not present in the initial set. For an m-equation problem with m different variables in the final basic set, the number of iterations may run anywhere from m as a minimum, to 2m and rarely to 3m. The number is usually less than 3m/2 when there are less than 50 equations and 200 variables (to judge from informal empirical observations). Some believe that on a randomly chosen problem with fixed m, the number of iterations grows in proportion to n.

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