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D. Nassimi, "Parallel Algorithms for the Classes of +or2^b DESCEND and ASCEND Computations on a SIMD Hypercube," IEEE Transactions on Parallel and Distributed Systems, vol. 4, no. 12, pp. 13721381, December, 1993.  
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@article{ 10.1109/71.250118, author = {D. Nassimi}, title = {Parallel Algorithms for the Classes of +or2^b DESCEND and ASCEND Computations on a SIMD Hypercube}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {4}, number = {12}, issn = {10459219}, year = {1993}, pages = {13721381}, doi = {http://doi.ieeecomputersociety.org/10.1109/71.250118}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Parallel and Distributed Systems TI  Parallel Algorithms for the Classes of +or2^b DESCEND and ASCEND Computations on a SIMD Hypercube IS  12 SN  10459219 SP1372 EP1381 EPD  13721381 A1  D. Nassimi, PY  1993 KW  Index Terms2/sup b/ permutation; SIMD hypercube; routing steps; fullduplex routing; parallelcomputations; efficient algorithm; +or2/sup b/ ascend; +or2/sup b/ descend; cyclicshift; oddeven merge; parallel prefix; PM2I interconnection; computational complexity;hypercube networks; parallel algorithms VL  4 JA  IEEE Transactions on Parallel and Distributed Systems ER   
Derives a simple lower bound for performing a 2/sup b/ permutation on an NPE SIMDhypercube, proving that log Nb routing steps are needed even if one allows an arbitrarymapping of elements to processors. An algorithm for performing a 2/sup b/ permutationusing exactly log Nb fullduplex routing steps that is slightly more efficient thanpreviously known O(log Nb) algorithms, which perform the permutation as an Omega orOmega /sup 1/ mapping, is presented. The author has also identified a general class ofparallel computations called +or2/sup b/ descend, which includes Batcher's oddevenmerge and many other algorithms. An efficient algorithm for performing any computation in this class in O(log N) steps on an NPE SIMD hypercube is given. A related class of parallel computations called +or2/sup b/ ascend is also defined. This class appears to be more difficult than +or2/sup b/ descend. A simple O(log/sup 2/ N/log log) N algorithm for this class on a SIMD hypercube, requiring Theta (log log N) space per processor is developed.
[1] K. E. Batcher, "Sorting networks and their applications," inProc. AFIPS 1968 Spring Joint Comput., vol. 32, 1968, pp. 307314.
[2] T. Y. Feng, "A survey of interconnection networks,"Computer, vol. 14, no. 12, pp. 1227, 1981.
[3] S. L. Johnsson, "Communication efficient basic linear algebra computations on hypercube architectures,"J. Parallel Distributed Comput., pp. 133172, 1987.
[4] D. E. Knuth,The Art of Computer Programming, Vol. 3, Reading, MA: AddisonWesley, 1973.
[5] M. Kumar and D. S. Hirschberg, "An efficient implementation of batcher's oddeven merge algorithm and its application in parallel sorting schemes,"IEEE Trans. Comput., vol. C32, pp. 254264, 1983.
[6] D. Lawrie, "Access and alignment of data in an array processor,"IEEE Trans. Comput., vol. C24, no. 12, pp. 11451155, 1975.
[7] D. Nassimi and S. Sahni, "Parallel permutation and sorting algorithms and a new generalized connection network,"J. ACM, vol. 29, no. 3, pp. 642667, 1982.
[8] D. Nassimi and Y. D. Tsai, "Efficient implementations of a class of±2bparallel computations on a SIMD hypercube," inProc. 5th Int. Parallel Processing Symp., Apr. 1991, pp. 29.
[9] D. Nassimi, "Nearly logarithmictime parallel algorithms for the class of±2bASCEND computations on a SIMD hypercube," inProc. 6th Int. Parallel Processing Symp., Mar. 1992, pp. 122129.
[10] D. Nassimi, "Parallel algorithms for PM2BASCEND computations on a SIMD hypercube using multiple levels of iterationgrouping," inProc. 1992 Int. Conf. Parallel Processing, Aug. 1992.
[11] F. P. Preparata and J. Vuillemin, "The cubeconnected cycle: A versatile network for parallel computation,"Commun. ACM, vol. 24, pp. 300309, May 1981.
[12] Y. Saad and M. H. Schultz, "Topological properties of hypercubes,"IEEE Trans. Comput., pp. 907913, 1988.
[13] H. J. Siegel, "Analysis techniques for SIMD machine interconnection networks and the effects of processor address masks,"IEEE Trans. Comput., vol. 26, no. 2, pp. 153161, 1977.
[14] H. Stone, "Parallel processing with the perfect shuffle,IEEE Trans. Comput., vol. C20, pp. 153161, 1971.