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

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

June 10 1994

## ABSTRACT

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.