Modulo Optimization Problems and Integer Linear Programming

Abstract

This chapter discusses modulo optimization problems and integer linear programming. A modulo optimization problem is the maximization of a linear functional of 0–1 variables subject to a system of linear modulo equations. The chapter explains the way to transform a modulo optimization problem to an integer linear programming problem with n variables and n pairs of linear inequality constraints. It is possible to exploit the special structure of the integer programming problem. An integer matrix is unimodular only if its determinant is equal to plus one or minus one. Any integer optimization problem with n variables, k linear inequalities, and modulo equations can be transformed to an equivalent integer programming problem with n variables and k linear inequalities.