A Mixed Integer Linear Programming Problem Which is Efficiently Solvable

Abstract

Efficient algorithms are known for the simple linear programming problem where each inequality is of the form xj-xi<=aij. Furthermore, these techniques extend to the integer linear programming variant of the problem. This paper gives an efficient solution to the mixed-integer linear programming variant where some, but not necessarily all, of the unknowns are required to be integers. The algorithm we develop is based on a graph representation of the constraint system and runs in O(|V||E|+|V|62lh|V|) time. It has several applications including optimal retiming of synchronous circuitry, VLSI layout compaction in the presence of power and ground buses, and PERT scheduling with periodic constraints.