Minimizing Buffer Requirements under Rate-Optimal Schedule in Regular Dataflow Networks

Large-grain synchronous dataflow graphs or multi-rate graphs have the distinct feature that the nodes of the dataflow graph fire at different rates. Such multi-rate large-grain dataflow graphs have been widely regarded as a powerful programming model for DSP applications. In this paper we propose a method to minimize buffer storage requirement in constructing rate-optimal compile-time (MBRO) schedules for multi-rate dataflow graphs. We demonstrate that the constraints to minimize buffer storage while executing at the optimal computation rate (i.e. the maximum possible computation rate without storage constraints) can be formulated as a unified linear programming problem in our framework. A novel feature of our method is that in constructing the rate-optimal schedule, it directly minimizes the memory requirement by choosing the schedule time of nodes appropriately. Lastly, a new circular-arc interval graph coloring algorithm has been proposed to further reduce the memory requirement by allowing buffer sharing among the arcs of the multi-rate dataflow graph. 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 (IEEE Transactions on Computers, vol. 36, no. 1, 1987, pp. 24–35), (ii) the optimal scheduling buffer allocation (OSBA) algorithm of Ning and Gao (Conference Record of the Twentieth Annual ACM SIGPLANSIGACT Symposium on Principles of Programming Languages, Charleston, SC, Jan. 10–13, 1993, pp. 29–42), and (iii) the multi-rate software pipelining (MRSP) algorithm (Govindarajan and Gao, in Proceedings of the 1993 International Conference on Application Specific Array Processors, Venice, Italy, Oct. 25–27, 1993, pp. 77–88). Schedules generated for a number of random dataflow graphs and for a set of DSP application programs using the different scheduling methods are compared. The experimental results have demonstrated a significant improvement (10–20%) in buffer requirements for the MBRO schedules compared to the schedules generated by ∗This work was done when the authors were at McGill University, Montreal, Canada, and the work was supported by research grants from Micronet—Network Centres of Excellence, Canada. †A preliminary version of this paper has appeared in the 1994 International Conference on Application Specific Array Processors, San Franscisco, August 1994. 208 Govindarajan, Gao and Desai the other three methods, without sacrificing the computation rate. The MBRO method also gives a 20% average improvement in computation rate compared to Lee’s Block scheduling method.