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Manipulating General Vectors on Synchronous Binary N-Cube
July 1993 (vol. 42 no. 7)
pp. 863-871

The author describes efficient manipulations of general vectors on the synchronous binary n-cube structure. A general vector is defined as a set of elements stored in consecutive processors with arbitrary length and starting point, and one element per processor. New routing methods for manipulating general vectors are presented. The author focuses on six major vector manipulating functions: merge, split, rotation, reverse, compression, and expansion. They are frequently used to extract and structure data parallelism in image processing and parallel solutions of linear systems. It is observed that varying the dimension order is a key to collision-free vector manipulations. A formal network model is developed for determining when link collisions occur. With the aid of this network model dimension orders yielding collision-free routine for the six manipulating functions are identified. Collision-free routing allows data communication to complete in the optimal time-single network cycle. The dimension orders are easy to encode and decode, and they are feasible for physical implementation.

[1] K. Padmanabhan, "Cube structure for multiprocessors,"Commun. ACM, vol. 33, pp. 43-52, 1990.
[2] D. H. Lawrie, "Access and alignment of data in array processors,"IEEE Trans. Comput., vol. C-24, no. 12, pp. 1145-1155, Dec. 1975.
[3] M. C. Pease, III, "The indirect binaryn-cube microprocessor array,"IEEE Trans. Comput., vol. C-26, no. 5, pp. 458-473, May 1977.
[4] Y. Lan and L. Ni, "Relay approach message routing in hypercube multiprocessors," inProc. 3rd Int. Conf. Supercomputing, vol. III, pp. 174-182, May 1988.
[5] Y. Saad and M. H. Schultz, "Data communication in hypercubes,"J. Parallel Distributed Comput., vol. 6, pp. 115-135, 1989.
[6] C. T. Ho and S. L. Johnsson, "Distributed routing algorithms for broadcasting and personalized communication in hypercubes," inProc. 1986 Int. Conf. Parallel Processing, pp. 640-648, Aug. 1986.
[7] T. Szymansky, "On the permutation capability of a circuit-switched hypercube," inProc. 1989 Int. Conf. Parallel Processing, vol. 1, pp. 103-110, Aug. 1989.
[8] J. L. Gustafson, G. R. Montry, and R. E. Benner, "Development of parallel methods for a 1024 processor hypercube,"SIAM J. Sci. Stat. Comput., vol. 9, no. 4, pp. 609-638, July 1988.
[9] W.J. Dally and C.L. Seitz, "Deadlock-Free Message Routing in Multiprocessor Interconnection Networks,"IEEE Trans. Computers, Vol. C-36, No. 5, May 1987, pp. 547-553.
[10] L. W. Tucker and G. G. Robertson, "Architecture and applications of the connection machine,"Computer, pp. 26-38, Aug. 1988.
[11] D. Nassimi and S. Sahni, "Optimal BPC permutations on a cube connected SIMD network,"IEEE Trans. Comput., pp. 338-341, Apr. 1982.
[12] C. S. Rghavendra and M. A. Sridhar, "Optimal routing of bit-permutes on hypercube machines," inProc. 1990 Int. Conf. Parallel Processing, pp. 286-290.
[13] S. Ranka and S. Sahni, "Hypercube algorithms for image transformation," inProc. 1989 Int. Conf. Parallel Processing, Aug. 1989, pp. 24-31.
[14] W. Lin, "A dimension-scrambling approach to fast hypercube data permutations," inProc. 1990 Int. Conf. Parallel Processing, Aug. 1990, pp. 119-122.
[15] R. K. Montoye and D. H. Lawrie, "A practical algorithm for the solution of triangular systems on a parallel processing system,"IEEE Trans. Comput., vol. C-31, no. 11, pp. 1076-1082, Nov. 1982.

Index Terms:
general vectors manipulation; encoding; decoding; synchronous binary n-cube; arbitrary length; merge; split; rotation; reverse; compression; expansion; data parallelism; image processing; collision-free vector manipulations; formal network model; collision-free routine; manipulating functions; data communication; optimal time-single network cycle; multiprocessor interconnection networks; vector processor systems.
Citation:
W. Lin, "Manipulating General Vectors on Synchronous Binary N-Cube," IEEE Transactions on Computers, vol. 42, no. 7, pp. 863-871, July 1993, doi:10.1109/12.237726
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