Abstract
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.
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Timothy O’Neil received his Ph.D. in Computer Science and Engineering from the University of Notre Dame in 2002, where he was awarded the Arthur J. Schmitt Fellowship. He also received master’s degrees in mathematics (1991) and computer and information sciences (1993) from The Ohio State University in Columbus, Ohio. He is presently an Assistant Professor in the Computer Science Department at the University of Akron. His current research interests include loop transformations and data scheduling.
Edwin Hsing-Mean Sha received the B.S.E. degree in computer science and information engineering from National Taiwan University, Taipei, Taiwan, in 1986; he received the M.A. and Ph.D. degree from the Department of Computer Science, Princeton University, Princeton, NJ, in 1991 and 1992, respectively. From August 1992 to August 2000, he was with the Department of Computer Science and Engineering at University of Notre Dame, Notre Dame, IN. He served as Associate Chairman for Graduate Studies from 1995 to 2000. Since 2000, he has been a tenured full professor in the Department of Computer Science at the University of Texas at Dallas.
He has published more than 170 research papers in referred conferences and journals. He has been serving as an editor for several journals such as IEEE Transactions on Signal Processing and Journal of VLSI Signal Processing. He also served as program committee members in numerous conferences. He received Oak Ridge Association Junior Faculty Enhancement Award in 1994, and NSF CAREER Award. He was a guest editor for the special issue on Low Power Design of IEEE Transactions on VLSI Systems in 1997. He also served as the program chairs for the International Conference on Parallel and Distributed Computing Systems (PDCS), 2000 and PDCS 2001. He received Teaching award in 1998.
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O’Neil, T.W., Sha, E.HM. Combining Extended Retiming and Unfolding for Rate-Optimal Graph Transformation. J VLSI Sign Process Syst Sign Image Video Technol 39, 273–293 (2005). https://doi.org/10.1007/s11265-005-4845-6
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DOI: https://doi.org/10.1007/s11265-005-4845-6