Long Monotone Paths in Abstract Polytopes

As is now well known, the simplex method, under its various pivoting rules, is not a “good algorithm” in the sense of J. Edmonds, i.e., the number of pivots needed to solve a given linear programming problem by this method cannot be bounded by a polynomial function of the number of rows and columns defining it, Klee, Minty and Jerosolow have developed methods for constructing examples of such linear programs on polytopes. The aim of this paper is to extend these constructions to abstract polytopes.