Abstract
Multidimensional computational models of two-level algorithms are introduced and investigated. Transformations of graph models of the algorithms are developed, which allow one to obtain modified models without global edges. The modified graph models can be transformed by the well-known transformation and mapping procedures into one-, two-, and three-dimensional array processors without global interconnections.
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References
V. V. Voyevodin, Mathematical Models and Methods in Parallel Processes [in Russian], Nauka, Moscow (1986).
S.-Y. Kung, VLSI Array Processors, Prentice-Hall, Englewood Cliffs, New Jersey (1988).
Yu. S. Kanevskii, Systolic Processors [in Russian], Tekhnika, Kiev (1991).
P. Lee and Z. Kedem, “Synthesizing linear array algorithms from nested for loop algorithms” IEEE Trans. Comput., 37, No. 12, 1578–1598 (1988).
W. Shang and J. A. Fortes, “On time mapping of uniform dependence algorithms into lower dimensional processor arrays,” IEEE Trans. Paral. Distrib. Syst. 3, No. 31, 350–363 (1992).
V. V. Kosianehouk, N. A. Likhoded, and P. I. Sobolevskii, “Systolic Architecture Array Synthesis,” Preprint Inst. Mat. AN Belarusi, No. 6 (484), Minsk (1992).
N. A. Likhoded and A. A. Tiunchik, “Method of constructing parallel forms of algorithms based on locally parallel, globally sequential partition,” Kibern. Sist. Anal., No. 2, 28–42 (1996).
W. Achtziger and K.-H. Zimmerman, “A branching linear programming approach for the mapping of systems ofn-dimensional affine recurrence ontok-dimensional systolic arrays,” Prepr. of the Institute of Applied Mathematics, No. 172, University of Erlangen-Nuremberg, Erlangen, Germany (1996).
A. A. Tiunchik, “Designing of multilevel systolic processors,” Dokl. NAN Belarusi,38, No. 4, 16–18 (1994).
A. A. Tiunchik, “Generalized approach to the design of VLSI array processors,” in: Proc. 7th Intern. Workshop on Parallel Processing by Cellular Automata and Arrays, Akademie Verlag, Berlin (1996), pp. 77–84.
R. M. Karp, R. E. Miller, and S. Winograd, “Organization of computations for uniform recurrence equations,” J. ACM,13, No. 3, 563–590 (1967).
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Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 63–71, November–December, 1999.
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Likhoded, N.A., Sobolevskii, P.I. & Tiunchik, A.A. Localization of edges in graph models of two-level algorithms. Cybern Syst Anal 35, 895–902 (1999). https://doi.org/10.1007/BF02742281
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DOI: https://doi.org/10.1007/BF02742281