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Optimal Broadcast in All-Port Wormhole-Routed Hypercubes
February 1995 (vol. 6 no. 2)
pp. 200-204

Abstract—We give an optimal algorithm that broadcasts on an $n$-dimensional hypercube in $\Theta(n/\log_2(n+1))$ routing steps with wormhole, $e$-cube routing and all-port communication. Previously, the best algorithm of McKinley and Trefftz requires $\lceil{n/2} \rceil$ routing steps. We also give routing algorithms that achieve tight time bounds for $n \le 7$.

[1] P.R. Cappelo, "Gaussian Elimination on Hypercube Automation," J. Parallel and Distributed Computing, no. 4, pp. 288-308, 1987.
[2] W. J. Dally,The {J-Machine}: System Support for Actors, Hewitt and Agha, Eds. Cambridge, MA: MIT Press, 1989,
[3] G. Foxet al.,Solving Problems on Concurrent Processors, vol. I. Englewood Cliffs, NJ: Prentice Hall, 1988.
[4] P. Fraigniaud and E. Lazard,“Methods and Problems of Communication in Usual Networks,”IMAG, Ecole Normale Sup\'erieure de Lyon, France, Tech. Rep. 91-33, Oct. 1991.
[5] D. Gannon and J. Van Rosendale,“On the impact of communication complexity in the design of parallel numerical algorithms,”IEEE Trans. Comput., 33(12):1180–1194, Dec. 1984.
[6] G. A. Geist and M. T. Heath, Ed.,“Matrix factorization on a hypercube multiprocessor,”inHypercube Multiprocessors 1986. SIAM, 1987, pp. 161–180.
[7] S. M. Hedetniemi, S. T. Hedetniemi, and A. L. Liestman,“A survey of gossiping and broadcasting in communication networks,”Networks, vol. 18, pp. 319–349, 1988.
[8] C.-T. Ho,“Optimal broadcasting on SIMD hypercubes without indirect addressing capability,”J. Parallel Distrib. Comput., 13(2):246–255, Oct. 1991.
[9] C.-T. Ho and M.-Y. Kao,“Optimal broadcast on hypercubes with wormhole and$e$-cube routings,”in1993 Int. Conf. Parallel and Distrib. Syst., Dec. 1993, pp. 694–697.
[10] C.-T. Ho and M.T. Raghunath, "Efficient Communication Primitives on Hypercubes," Concurrency: Practice and Experience, vol. 4, no. 6, pp. 427-458, Sept. 1992.
[11] Intel Corporation, A Touchstone DELTA System Description, 1991.
[12] S.L. Johnsson, "Communication Efficient Basic Linear Algebra Computations on Hypercube Architectures," J. Parallel and Distributed Computing, vol. 4, pp. 133-172, 1987.
[13] S. L. Johnsson and C.-T. Ho,“Matrix multiplication on Boolean cubes using generic communication primitives,”inParallel Processing and Medium-Scale Multiprocessors, A. Wouk, Ed. SIAM, 1989, pp. 108–156.
[14] S. L. Johnsson and C.-T. Ho,“Optimum broadcasting and personalized communication in hypercubes,”IEEE Trans. Comput.,vol. 38, pp. 1249–1268, Sept. 1989.
[15] P. K. McKinley and C. Trefftz,“Efficient broadcast in all-port wormhole-routed hypercubes,”in1993 Int. Conf. Parallel Process., vol. II, Aug. 1993, pp. 288–291.
[16] C. Moler,“Matrix computation on distributed memory multiprocessors,”inHypercube Multiprocessors 1986, M. T. Heath, Ed., SIAM, pp. 181–195, 1987.
[17] L. M. Ni and P. McKinley,“A survey of wormhole routing techniques in direct networks,”IEEE Comput., 26(2):62–76, Feb., 1993.
[18] J.-Y. L. Park, S.-K. Lee, and H.-A. Choi,“New algorithms for broadcasting in Meshes,”George Washington University, Tech. Rep. GWU-IIST-93-03, 1993.
[19] J. Peters and M. Syska,“Circuit-switched broadcasting in torus networks,”Simon Fraser University, Tech. Rep. CMPT TR 93-04, May 1993.
[20] D.F. Robinson, D. Judd, P.K. McKinley, and B.H.C. Cheng, “Efficient Collective Data Distribution in All-Port Wormhole-Routed Hypercubes,” Proc. Supercomputing Conf., pp. 792–801, Nov. 1993.
[21] H. Sullivan and T.R. Bashkow, "A Large Scale, Homogenous, Fully Distributed Parallel Machine," Proc. Fourth Ann. Int'l Symp. Computer Architecture, pp. 105-117, May 1977.

Ching-Tien Ho, Ming-Yang Kao, "Optimal Broadcast in All-Port Wormhole-Routed Hypercubes," IEEE Transactions on Parallel and Distributed Systems, vol. 6, no. 2, pp. 200-204, Feb. 1995, doi:10.1109/71.342134
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