Retiming synchronous data-flow graphs to reduce execution time

Abstract

Many common iterative or recursive DSP applications can be represented by synchronous data-flow graphs (SDFGs). A great deal of research has been done attempting to optimize such applications through retiming. However, despite its proven effectiveness in transforming single-rate data-flow graphs to equivalent DFGs with smaller clock periods, the use of retiming for attempting to reduce the execution time of synchronous DFGs has never been explored. In this paper, we do just this. We develop the basic definitions and results necessary for expressing and studying SDFGs. We review the problems faced when attempting to retime a SDFG in order to minimize clock period, then present algorithms for doing this. Finally, we demonstrate the effectiveness of our methods on several examples.

Contention-conscious transaction ordering in multiprocessor DSP systems

“…Useful directions for further work include incorporating transaction ordering considerations into the scheduling process; integrating transaction ordering and retiming of synchronous dataflow graphs [30]; the exploration of hybrid scheduling strategies that can combine ordered transaction, self-timed, and fully-static strategies in the same implementation based on subsystem characteristics; and extension to more general DSP modeling techniques, such as stream-based functions [31], cyclo-static dataflow [32], multidimensional dataflow [33], and parameterized dataflow [34].…”

Resource-Constrained Static Scheduling of Synchronous Data-Flow Graphs

“…(The reverse is not necessarily true, as shown in [12].) If this condition holds there is a positive integer vector q in the nullspace of the topology matrix called a repetition vector for G. The repetition vector for G with the smallest norm is called the basic repetition vector (BRV) for G [1].…”

“…The average computation time of an iteration is called the iteration period of the SDFG. If a SDFG G contains a loop, then the iteration period is bounded from below by the iteration bound [13] of G (sometimes referred to as the maximum cycle mean of G), which is denoted B(G) and defined to be the maximum time-to-delay ratio of all cycles in G. While complicated to derive for SDFGs in general, as shown in [11], we can quickly estimate this value.…”

“…Since liveness is an important property when studying SDFGs, developing an efficient test is crucial. One simple test from [11] is outlined below.…”

“…Prior to our exploration of the subject [11,12], the most common method for manipulating and scheduling SDFGs was to translate the SDFG to its single-rate equivalent (i.e. a traditional DFG with trivial production and consumption rates) and work with this new graph.…”