A recursive technique for computing lower-bound performance of schedules

Abstract

We present a fast recursive technique for estimating lower-bound performance of data path schedules. The method relies on the determination of an ASAPUC (As Soon As Possible Under Constraint) time-step value for each node of the DFG (Data-Flow Graph) that is based on the ASAPUC values of its predecessor nodes. That is, the lower-bound estimation is applied to each subgraph permitting the derivation of a tight lower bound on the performance of the complete DFG. Applying the greedy lower-bound estimator of Rim and Jain [1994] to each subgraph improves the complete lower bound in more than 50% of the experiments reported in Rim and Jain [1994], and the CPU time is only about twice as long. The recursive methodology can be extended to exploit other lower-bound techniques, for example, considering other constraints such as the number of busses or registers.

On lower bounds for scheduling problems in high-level synthesis

“…It is easy to see that the bounds derived by Rim and Jain [11] are the same as the bounds obtained from LowerBoundT ; ASAP; U B , ALAP; U B , and that the bounds computed by Langevin and Cerny [6] is the same as the bounds obtained from LowerBoundT ; H1; U B , ALAP. Therefore, the bounds obtained from the procedure shown above are tighter than the bounds obtained by Langevin and Cerny [6] which in turn are tighter than those obtained by Rim and Jain [11].…”

“…Therefore, the bounds obtained from the procedure shown above are tighter than the bounds obtained by Langevin and Cerny [6] which in turn are tighter than those obtained by Rim and Jain [11].…”

“…In this paper, we present new bounds and a theoretical comparison of these with existing bounds. For the resourceconstrained 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.…”

“…Chaudhuri and Walker [1] and Hu et al [4] have shown algorithms for computing lower bounds for the TimeConstrained Scheduling problem. Rim and Jain [11] and Langevin and Cerny [6] have shown algorithms for computing lower bounds for the Resource-Constrained Scheduling problem. Several authors [5,9,10,12] have shown different algorithms that compute lower bounds for both these problems or for related problems.…”

An integer programming approach to optimal basic block instruction scheduling for single-issue processors

“…In 1996, Langevin and Cerny [21] proposed to apply this method recursively, namely to each sub-DAG induced by interpreting each predecessor of an instruction i ∈ I as the sink prior to running the algorithm on the (sub-)DAG with sink i. This way, improved lower bounds on the issue cycles of predecessors of i will be already respected when computing a lower bound on i's issue cycle.…”