Parametric integer programming

Abstract

When analysing computer programs (especially numerical programs in which arrays are used extensively), one is often confronted with integer programming problems. These problems have three peculiarities: ffl feasible points are ranked according to lexicographic order rather than the usual linear economic function; ffl the feasible set depends on integer parameters; ffl one is interested only in exact solutions. The difficulty is somewhat alleviated by the fact that problems sizes are usually quite small. In this paper we show that: ffl the classical simplex algorithm has no difficulty in handling lexicographic ordering; ffl the algorithm may be executed in symbolic mode, thus giving the solution of continuous parametric problems; ffl the method may be extended to problems in integers. We prove that the resulting algorithm always terminate and give an estimate of its complexity. R'esum'e L'analyse s'emantique des programmes (sp'ecialement des programmes num'eriques utilisant de...