On the Optimal Blocking Factor for Blocked, Non-Overlapped Schedules 1

Praveen Murthy and Edward A. Lee

Memo. No. UCB/ERL M94/46, Electronics Research Laboratory, College of Engineering, UC Berkeley, CA 94720
June 10 1994



This paper addresses the problem of determining the optimal blocking factor for blocked, non-overlapped multiprocessor schedules for signal processing programs expressed as synchronous dataflow (SDF) graphs. One approach to determining a multiprocessor schedule for an SDF graph G is to determine a schedule for the J-unfolded graph of G (defined to be the precedence graph of G over J iterations), where J 1, and repeat that schedule forever. This approach allows us to exploit some of the inter-iteration parallelism that is usually present in the SDF graph. A schedule for the J-unfolded graph is called a schedule of blocking factor . It is of interest to determine the value of J that will allow schedules of optimal throughput to be constructed. It will be shown that the critical path of the J-unfolded graph becomes cyclic as J is increased. It will be shown that it is possible to determine this cyclicity by analyzing the critical graph of a matrix that arises in the model that is used. The cyclicity of the critical path implies that we only have to examine a finite number of blocking factors to determine the optimal one.