Gröbner Bases in Integer Programming

Abstract

Recently, application of the theory of Gröbner bases to integer programming has given rise to new tools and results in this field. Here we present this algebraic theory as the natural integer analog of the simplex approach to linear programming Although couched in algebra, the theory of Gröbner bases and its consequences for integer programming are intimately intertwined with polyhedral geometry and lattice arithmetic which are staples of the traditional approach to this subject.