On lower bounds for scheduling problems in high-level synthesis

This paper presents new results on lower bounds for the scheduling problem in high-level synthesis. While several techniques exist for lower bound estimation, comparisons among the techniques have been experimental with few guarantees on the quality of the bounds. In this paper, we present new bounds and a theoretical comparison of these with existing bounds. For the resource-constrained scheduling problem, we present a new algorithm which generalizes the bounding techniques of Langevin and Cerny [6] and Rim and Jain [11]. This algorithm is shown to produce bounds that are provably tighter than other existing techniques. For the time constrained scheduling problem, we show how to generate the tightest possible bounds that can be derived by ignoring the precedence constraints by solving a linear programming formulation. These bounds are therefore guaranteed to be tighter than the bounds generated by the techniques of Fernandez-Bussell [2] or Sharma-Jain [12]. As a result, we show that the linear relaxation of the ILP formulation of the time constrained scheduling problem produces tighter bounds than the two techniques mentioned above.