We present an efficient algorithm to find an optimal integer solution of a given system of 2-variable equalities and 1-variable inequalities with respect to a given linear objectiv...
Integer programs defined by two equations with two free integer variables and nonnegative continuous variables have three types of nontrivial facets: split, triangle or quadrilat...
In recent years there has been growing interest in generating valid inequalities for mixedinteger programs using sets with 2 or more constraints. In particular, Andersen et al. (2...
We introduce a calculus for handling integer arithmetic in first-order logic. The method is tailored to Java program verification and meant to be used both as a supporting procedur...
A central result in the theory of integer optimization states that a system of linear diophantine equations Ax = b has no integral solution if and only if there exists a vector in...
Kent Andersen, Quentin Louveaux, Robert Weismantel