Finding a bounded mixed-integer solution to a system of dual network inequalities

Abstract

We show that using max-algebraic techniques it is possible to generate the set of all solutions to a system of inequalities x i − x j ≥ b i j , i , j = 1 , … , n using n generators. This efficient description enables us to develop a pseudopolynomial algorithm which either finds a bounded mixed-integer solution, or decides that no such solution exists.