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Optimal Algorithms on the Pipelined Hypercube and Related Networks
May 1993 (vol. 4 no. 5)
pp. 582-591

Parallel algorithms for several important combinatorial problems such as the all nearest smaller values problem, triangulating a monotone polygon, and line packing are presented. These algorithms achieve linear speedups on the pipelined hypercube, and provably optimal speedups on the shuffle-exchange and the cube-connected-cycles for any number p of processors satisfying 1>or=p>or=n/((log/sup 3/n)(loglog n)/sup 2/), where n is the input size. The lower bound results are established under no restriction on how the input is mapped into the local memories of the different processors.

[1] O. Berkman, B. Schieber, and U. Vishkin, "Some doubly logarithmic optimal parallel algorithms based on finding all nearest smaller values," UMIACS-TR-88-79, Univ. Maryland, 1988.
[2] R. P. Brent, "The parallel evalution of general arithmetic expressions,"J. ACM, vol. 21, pp. 201-206, 1974.
[3] S.-C. Chang and J. JáJá, "Parallel algorithms for channel routing in the knock-knee model,"SIAM J. Comput., to be published. Also available inProc. 1988 Int. Conf. Parallel Processing.
[4] S.-C. Chang, J. JáJá, and K. W. Ryu, "Optimal parallel algorithms for one-layer routing," Tech. Rep. UMIACS-TR-89-46, CS-TR-2239, Univ. Maryland, Apr. 1989.
[5] R. Cypher and J. L. C. Sanz, "Cubesort: An optimal sorting algorithm for feasible parallel computers," inProc. 1988 ICPP, 1988, pp. 308-311.
[6] R. Cypher and C. G. Plaxton, "Deterministic sorting in nearly logarithmic time on the hypercube and related computers," inProc. 22nd ACM Symp. Theory Comput., 1990, pp. 193-203.
[7] E. Dekel and S. Sahni, "Parallel scheduling algorithms,"Oper. Res., vol. 31, no. 1, Jan.-Feb. 1983.
[8] J. R. Gilbert, "Graph separator theorems and sparse Gaussian elimination," Ph.D. dissertation, Standord Univ., 1980.
[9] K. T. Herley and G. Bilardi, "Deternistic simulations of PRAMs" inProc. 26th Allerton Conf. Commun., Contr. and Comput., 1988, pp. 1084-1093.
[10] K. T. Herley, "Bounded degree networks," inProc. 1989 IEEE Symp. Foundations on Comput. Sci., pp. 390-395.
[11] D. Hoey and C. E. Leiserson, "A layout for the shuffle-exchange network," inProc. 1980 ICCP, 1980, pp. 329-336.
[12] J. JáJá,An Introduction to Parallel Algorithms. Reading, MA: Addison-Wesley, 1992.
[13] J. JáJáand K. W. Ryu, "Load balancing and routing on the hypercube and related networks," inProc. 1990 Int. Conf. Parallel Processing, Also,J. Parallel and Distributed Comput., to be published.
[14] C. E. Leiserson, "Area-efficient layouts (for VLSI)," inProc. 21st Annu. Symp. Foundations of Comput. Sci., IEEE, Syracuse, NY, 1980, pp. 270-281.
[15] D. Nassimi and S. Sahni, "Parallel permutation and sorting algorithms and a new generalized connection network,"J. ACM, vol. 29, no. 3, pp. 642-667, 1982.
[16] G. Plaxton, "Load balancing, selection and sorting on the hypercube," inProc. 1st ACM Symp. Parallel Algorithms and Architectures, June 1989, pp. 64-73.
[17] F. P. Preparata and J. Vuillemin, "The cube-connected cycle: A versatile network for parallel computation,"Commun. ACM, vol. 24, pp. 300-309, May 1981.
[18] B. Schieber and U. Vishkin, "Finding all nearest neighbors for convex polygons in parallel: A new lower bound technique and a matching algorithm," UMIACS-tr-88-82, CS-TR-2138, Univ. Maryland, Nov. 1988.
[19] H. S. Stone, "Parallel processing with the perfect shuffle,"IEEE Trans. Comput., vol. C-20, no. 2, pp. 153-161, Feb. 1971.
[20] J. D. Ullman,Computational Aspects of VLSI. Rockville, MD: Computer Science Press, 1984.
[21] P. Varman and K. Doshi, "Sorting with linear speedup in a VLSI network," inProc. 1988 Int. Conf. Parallel Processing, 1988, pp. 202-206.

Index Terms:
Index Termsparallel algorithms; pipelined hypercube; combinatorial problems; monotone polygon; line packing; shuffle-exchange; cube-connected-cycles; combinatorial mathematics; computational geometry; parallel algorithms; pipeline processing
Citation:
J. JáJá, K.W. Ryu, "Optimal Algorithms on the Pipelined Hypercube and Related Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 4, no. 5, pp. 582-591, May 1993, doi:10.1109/71.224210
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