The existence of a strongly polynomial time simplex method

It is well known how to clarify whether there is a polynomial time simplex algorithm for linear programming (LP) is the most challenging open problem in optimization and discrete geometry. This paper gives a affirmative answer to this open question by the use of the parametric analysis technique that we recently proposed. We show that there is a simplex algorithm whose number of pivoting steps does not exceed the number of variables of a LP problem.