Timothy W. O'Neil

Combining Extended Retiming and Unfolding for Rate-Optimal Graph Transformation

Many computation-intensive iterative or recursive applications commonly found in digital signal processing and image processing applications can be represented by data-flow graphs (DFGs). The execution of all tasks of a DFG is called an iteration, with the average computation time of an iteration the iteration period. A great deal of research has been done attempting to optimize such applications by applying various graph transformation techniques to the DFG in order to minimize this iteration period. Two of the most popular are retiming and unfolding, which can be performed in tandem to achieve an optimal iteration period. However, the result is a transformed graph which is much larger than the original DFG. To the authors’ knowledge, there is no technique which can be combined with minimal unfolding to transform a DFG into one whose iteration period matches that of the optimal schedule under a pipelined design. This paper proposes a new technique, extended retiming, which does just this. We construct the appropriate retiming functions and design an efficient retiming algorithm which may be applied directly to a DFG instead of the larger unfolded graph. Finally, we show through experiments the effectiveness of our algorithms.

PARALLELIZING SYNCHRONOUS DATA-FLOW GRAPHS VIA RETIMING

Many common iterative or recursive DSP applications can be represented by synchronous dataflow graphs (SDFGs). A great deal of research has been done attempting to optimize such applications through retiming. However, despite its proven effectiveness in transforming singlerate 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 an algorithm for doing this. Finally, we demonstrate the effectiveness of our method on several examples.

Unfolding probabilistic data-flow graphs under different timing models

It is known that in many applications, because of selection statements, e.g., if-statement, the computation time of a node can be represented by a random variable. This paper focuses on any iterative application (containing loops) reflecting those uncertainties. Such an application can then be transformed to a probabilistic data-flow graph. A challenging problem is to derive graph transformation techniques which can produce a good schedule. This paper introduces two timing models, the time-invariant and time-variant models, to characterize the nature of these applications. Furthermore, for the time-invariant model, we propose a means of selecting a minimum rate-optimal unfolding factor which guarantees the best schedule length. We also propose a good estimation for choosing an unfolding factor for a graph under the time-variant model.