Analyzing and Exploiting the Structure of theConstraints in the ILP Approach to theScheduling

| In integer linear programming (ILP), formulating a \good" model is of crucial importance to solving that model 1]. In this paper, we begin with a mathematical analysis of the structure of the assignment, timing, and resource constraints in high-level synthesis, and then evaluate the structure of the scheduling polytope described by these constraints. We then show how the structure of the constraints can be exploited to develop a well-structured ILP formulation, which can serve as a solid theoretical foundation for future improvement. As a start in that direction, we also present two methods to further tighten the formulation. The contribution of this paper is twofold: (1) it provides the rst in-depth formal analysis of the structure of the constraints, and it shows how to exploit that structure in a well-designed ILP formulation, and (2) it shows how to further improve a well-structured formulation by adding new valid inequalities.