The Simplex Method and 0-1 Polytopes
نویسندگان
چکیده
We will derive two results of the primal simplex method by constructing simple LP instances on 0-1 polytopes. First, for any 0-1 polytope and any of its two vertices, we can construct an LP instance for which the simplex method finds a path between them, whose length is at most the dimension of the polytope. This proves a well-known result that the diameter of any 0-1 polytope is bounded by its dimension. Next we show that the upper bound for the number of distinct solutions generated by the simplex method is tight. We prove these results by using a basic property of the simplex method.
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