On the Variance of the Number of Pivot Steps Required by the Simplex Algorithm
Introduction: Despite their very good empirical performance the known variants of the simplex algorithm require exponentially many pivot steps in terms of the problem dimensions of the given linear programming problem (LPP) in worst-case situtation. The first to explain the large gap between practical experience and the disappointing worstcase was Borgwardt (1982a,b), who could prove polynomiality on the average for a certain variant of the algorithm—the “Schatteneckenalgorithmus (shadow vertex algorithm)”—using a stochastic problem simulation.
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