Minimizing Buuer Requirements under Rate-optimal Schedule in Regular Dataaow Networks

Large-grain synchronous data ow graphs or multi-rate graphs have the distinct feature that the nodes of the data ow graph re at di erent rates. Such multi-rate large-grain data ow graphs have been widely regarded as a powerful programming model for DSP applications. In this paper we propose a method to minimize bu er storage requirement in constructing rate-optimal compile-time (MBRO) schedules for multi-rate data ow graphs. We demonstrate that the constraints to minimize bu er storage while executing at the optimal computation rate (i.e. the maximum possible computation rate without storage constraints) can be formulated as a uni ed linear programming problem in our framework. A novel feature of our method is that it tries to minimize the memory requirement while simultaneously maximizing the computation rate. We have constructed an experimental testbed which implements our MBRO scheduling algorithm as well as (i) the widely used periodic admissible parallel schedules (also known as block schedules) proposed by Lee and Messerschmitt [16], (ii) the optimal scheduling bu er allocation (OSBA) algorithmof Ning and Gao [19], and (iii) the multirate software pipelining (MRSP) algorithm [9]. Schedules generated for a number of random data ow graphs and for a set of DSP application programs using the di erent scheduling methods are compared. The experimental results have demonstrated a signi cant improvement in bu er requirements for the MBRO schedules compared to the schedules generated by the other three methods. Compared to block schedules, MBRO schedules perform better in terms of both computation rate and bu er requirements. The average observed improvement in bu er storage is 26% with respect to the MRSP algorithm, 17% with respect to block schedules and 5% with respect to the OSBA formulation. At best, an MBRO schedule can perform with only 50% of the bu er requirement for an MRSP schedule or for a block schedule and without compromising the computation rate.