Regular Stream Flow Graphs 42 . 1 Operational Model of Regular Stream Flow

In this paper, we present a novel framework of multi-rate scheduling of signal processing programs represented by regular stream ow graphs (RSFGs). The main contribution of this paper is translating the scheduling problem of RSFGs into an equivalent problem in the domain of Karp-Miller computation graphs. A distinct feature of our scheduling framework | called multi-rate software pipelining | is to allow maximum overlapping of operations from successive iterations subject only to precedence constraints caused by data dependences. Our framework combines the insights and experience from two seemingly di erent lines of research: static scheduling of application-speci c programs and software pipelining of loops in general-purpose parallelizing compilers. We demonstrate that the scheduling of regular stream ow graphs can be formulated as a mathematical problem by capturing data dependencies between two actors as a precedence relation between the ring of these actors. Using linear schedules, the problem is further translated into a linear programming formulation. An e cient solution for the linear programming problem is obtained by rst constructing what is called the precedence graph. The precedence graphs are similar to the Karp-Miller computation graphs. A polynomial-time solution is obtained by observing that the computation rate of the optimal schedule is the minimum cost-to-time ratio cycle (MCTRC) in the precedence graph and using the well-established solution methods for the MCTRC problem. Finally, a graph coloring method based on the cyclic interval graph representation has been proposed to minimize the bu er space requirement for rate-optimal schedules. i