A Fast Algorithm for the Two-Variable Integer Programming Problem

An algorithm that solves any two-variable integer programming problem is presented. A constant word-length model for the data is assumed. The complexity for a problem with m constraints and word length of L digits iS bounded by the maximum of two values. The first, which is O(mlogm) steps, is a bound on the complexity of finding the convex region bounded by the constraints, each step being an arithmetic orperation or a compare. The second, which Is O(mL) steps, is the complexity of solving m greatest-common-divisor problems. The algorithm finds a minimal binding set of constraints for any given problem, in addition to finding the soluuon set. A new method of solving three constraint problems is introduced.