Fourier-Motzkin Elimination and Its Dual with Application to Integer Programming

Abstract

Research on linear inequalities systems prior to 1947 consisted of isolated efforts “by a few investigators. A case in point is the elimination technique for reducing the number of variables in the system. A description of the method can “be found in Fourier [1], Dines [2], and Motzkin [3]. It differs from its analog for systems of equations in that (unfortunately) each step in the elimination can greatly increase the number of inequalities in the remaining variables. For years the method was referred to as the Motzkin Elimination Method. However, because of the odd grave-digging custom of looking for artifacts in long forgotten papers, it is now known as the Fourier-Motzkin Elimination Method and perhaps will eventually be known as the Fourier-Dines-Motzkin Elimination Method.

Research and reproduction of this report was partially supported by U.S. Office of Naval Research under contract N-00014-67-A-0112-0011, U.S. Atomic Energy Commission Contract AT(04-3)-326 PA No. 18, National Science Foundation Grants GP 31393, and GP 34559, and Army Research Office — Durham DAHC-71-C-0041. Originally published in Journal of Combinatorial Theory, Vol. 14, No. 3, 1973, 288–297.