Optimum Broadcasting and Personalized Communication in Hypercubes

IEEE Transactions on Computers

Volumn 38, Issue 9, 1989, Pages 1249-1268

  Lennart Johnsson, S ^a   Ho, Ching Tien ^a  

^a YALE UNIVERSITY   (United States)

Author keywords

Balanced trees; binomial trees; Boolean cubes; broadcasting; multicast; personalized communication; routing

Indexed keywords

BROADCASTING; COMPUTER ARCHITECTURE; COMPUTER NETWORKS--PERFORMANCE; MATHEMATICAL TECHNIQUES--TREES;

BALANCED TREES; BINOMIAL TREES; BOOLEAN CUBES; PERSONALIZED COMMUNICATION;

COMPUTERS, DIGITAL;

EID: 0024735141     PISSN: 00189340     EISSN: None     Source Type: Journal    
DOI: 10.1109/12.29465     Document Type: Article

References (36)

1. A.V. Aho, J.E. Hopcroft, and J.D. Ullman, The Design and Analysis of Computer Algorithms. Reading, MA: Addision-Wes- ley, 1974.
2. S.N. Bhatt, F.R.K. Chung, F.T. Leighton, and A.L. Rosenberg, “Optimal simulations of tree machines,” in Proc. 27th IEEE Symp. Foundations Comput. Sci., 1986, pp. 274–282.
3. S.N. Bhatt and I.I.F. Ipsen, “How to embed trees in hypercubes,” Tech. Rep. YALEU/CSD/RR-443, Dept. Comput. Sci., Yale Univ., Dec. 1985.
4. S.A. Browning, “The tree machine: A highly concurrent computing environment,” Tech. Rep. 1980:TR:3760, Comput. Sci., California Instit. Technol., Jan. 1980.
5. E. Dekel, D. Nassimi, and S. Sahni, “Parallel matrix and graph algorithms,” SIAM J. Comput., vol. 10, pp. 657–673, 1981.
6. S.R. Deshpande and R.M. Jenevin, “Scaleability of a binary tree on a hypercube,” in Proc. Int. Conf. Parallel Processing, 1986, pp. 661–668.
7. M.J. Fischer, Efficiency of Equivalence Algorithms. New York: Plenum, 1972, pp. 153–167.
8. G.C. Fox and W. Furmanski, “Optimal communication algorithms on hypercube,” Tech. Rep. CCCP-314, California Instit. Technol., July 1986.
9. G.C. Fox and D. Jefferson, “Concurrent processor load balancing as a statistical physics problem,” Tech. Rep. CCCP-172, California Instit. Technol., May 1985.
10. D. Gannon and J. Van Rosendale, “On the impact of communication complexity in the design of parallel numerical algorithms,” IEEE Trans. Comput., vol. C-33, pp. 1180–1194, Dec. 1984.
11. J.L. Gustafson, S. Hawkinson, and K. Scott, “The architecture of a homogeneous vector supercomputer,” in Proc. 1986 Int. Conf. Parallel Processing, 1986, pp. 649–652.
12. J.P. Hayes, T.N. Mudge, Q.F. Stout, S. Colley, and J. Palmer, “Architecture of a hypercube supercomputer, in Proc. 1986 Int. Conf. Parallel Processing, 1986, 653–660.
13. W.D. Hillis, The Connection Machine. Cambridge, MA: MIT Press, 1985.
14. C.T. Ho and S.L. Johnsson, “Distributed routing algorithms for broadcasting and personalized communication in hypercubes,” in Proc. 1986 Int. Conf. Parallel Processing, 1986, pp. 640–648, Tech. Rep. YALEU/DCS/RR-483, May 1986.
15. C.T. Ho and S.L. Johnsson, “Spanning balanced trees in Boolean cubes,” Tech. Rep. YALEU/DCS/RR-508, Dept. Comput. Sci., Yale Univ., Jan. 1987.
16. Intel iPSC System Overview, Intel Corp., Jan. 1986. SIAM J. Sci. Stat. Comput., to be published.
17. S.L. Johnsson, “Communication efficient basic linear algebra computations on hypercube architectures,” J. Parallel Distrib. Comput., vol. 4, pp. 133–172, Apr. 1987. Rep. YALEU/DCS/RR-361, Jan. 1985.
18. S.L. Johnsson, “Ensemble architectures and their algorithms: An overview,” in Proceedings of the IMA Workshop Numerical Algorithms Par. Comput. Architectures, H. Schultz Ed., Berlin, Germany:Springer-Verlag, 1987. YALE/DCS/RR-580. Revision of YALE/DCS/RR-367, Feb. 1985.
19. S.L. Johnsson, “Odd-even cyclic reduction on ensemble architectures and the solution tridiagonal systems of equations,” Tech. Rep. YALE/DCS/ RR-339, Dep. Comput. Sci., Yale Univ., Oct. 1984.
20. S.L. Johnsson, “Solving tridiagonal systems on ensemble architectures,” SIAM J. Sci. Stat. Comp., vol. 8, pp. 354–392, May 1987; Rep. YALEU/DCS/RR-436, Nov. 1985.
21. S.L. Johnsson and C.T. Ho, “Algorithms for multiplying matrices of arbitrary shapes using shared memory primitives on a Boolean cube,” Tech. Rep. YALEU/DCS/RR-569, Dep. Comput. Sci., Yale Univ., Oct. 1987. Revision of YALE/DCS/RR-530. Presented at the ARMY Workshop on Medium Scale Parallel Processors, Stanford Univ., Jan. 1986.
22. S.L. Johnsson and C.T. Ho, Matrix transposition on Boolean n-cube configured ensemble architectures,” SIAM J. Matrix Anal. Appl., vol. 9, pp. 415–454, July 1988. YALE/DCS/RR-572. rev. ed. YALEU/DCS/RR-494 Nov. 1986, to be published.
23. S.L. Johnsson and C.T. Ho, “Multiple tridiagonal systems, the alternating direction method, and Boolean cube configured multiprocessors,” Tech. Rep. YALEU/ DCS/RR-532, Yale Univ., June 1987. SIAM J. Sci. Stat. Comput., to be published.
24. S.L. Johnsson and C.T. Ho, “Spanning graphs for optimum broadcasting and personalized communication in hypercubes,” Tech. Rep. YALEU/DCS/RR-500, Dep. Comput. Sci., Yale Univ., Nov. 1986.
25. F.T. Leighton, Complexity Issues in VLSI: Optimal Layouts for the Shuffle-Exchange Graph and Other Networks. Cambridge, MA: MIT Press, 1983.
26. O.A. McBryan and E.F. Van de Velde, “Hypercube algorithms and implementations,” SIAM J. Scientif. Statist. Comput., vol. 8, pp. s227-s287, Mar. 1987.
27. E.M. Reingold, J. Nievergelt, and N. Deo, Combinatorial Algorithms. Englewood Cliffs, NJ: Prentice-Hall, 1977.
28. Y. Saad and M.H. Schultz, “Data communication in hypercubes,” Tech. Rep. YALEU/DCS/RR-428, Dep. Comput. Sci., Yale Univ., Oct. 1985.
29. Y. Saad and M.H. Schultz, “Topological properties of hypercubes,” Tech. Rep. YALEU/ DCS/RR-389, Dep. Comput. Sci., Yale Univ., June 1985.
30. C.L. Seitz, “The cosmic cube,” Commun. ACM, vol. 28, pp. 22–33, 1985.
31. Q.F. Stout and B. Wager, “Passing messages in link-bound hypercubes,” in Proc. 1986 Hypercube Conf, SIAM, 1987.
32. L. Valiant and G.J. Brebner, “Universal schemes for parallel communication,” in Proc. 13th ACM Symp. Theory of Computat., ACM, 1981, pp. 263–277.
33. A.Y. Wu, “Embedding of tree networks in hypercubes,” J. Parallel Distrib. Comput., vol. 2, pp. 238–249, 1985.
34. J. Aubert and B. Schneider, “Decomposition de la somme cartesienne d'un cycle et de l'union de deux cycles hamiltoniens en cycles hamiltoniens,” Discrete Math., vol. 38, pp. 7–16, 1982.
35. M. Foregger, “Hamiltonian decompositions of products of cycles,” Discrete Math., vol. 24, pp. 251–260, 1978.
36. A.S. Wagner, personal communication, 1988.