Optimal parallel execution of complete binary trees and grids into most popular interconnection networks

  • E. Bampis
  • J. -C. König
  • D. Trystram
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 817)


In this paper, we consider an extension of the well known PRAM model for parallel distributed-memory computers using local communications. We present scheduling algorithms for the execution of complete binary trees on hypercube, de Bruijn, linear and grid interconnection networks on this model. We also show that a two dimensional grid precedence graph can be executed in optimal time on all these networks.

Key Words

PRAM parallel algorithms scheduling interconnection networks 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R.J. Anderson, P. Beame, W. Ruzzo, Low Overhead Parallel Schedules for Task Graphs, Proc. SPAA (1990).Google Scholar
  2. [2]
    E. Bampis, J-C. König, D. Trystram, A Low overhead schedule for a 3D-Grid Graph, Parallel Processing Letters Vol. 2, Nℴ 4, (1992) pp 363–372.CrossRefGoogle Scholar
  3. [3]
    N.G. De Bruijn, A Combinatorial Problem, Koninlijke Nederlandsa Academie van Wettenschappen Proc., Ser. A49, 758–764, (1946).Google Scholar
  4. [4]
    S.H. Bokhari, On the Mapping Problem, IEEE Trans. Comput. C-30, (1981), pp 207–214.Google Scholar
  5. [5]
    E.G. Coffman, P.J. Denning, Operating Systems Theory, Prentice Hall (1972).Google Scholar
  6. [6]
    M. Cosnard, A. Ferreira, Designing parallel non numerical algorithms, in Parallel Computing '91, Eds. D.J. Evans et coll., North Holland (1991) pp 3–18.Google Scholar
  7. [7]
    A. Gibbons, W. Rytter, Efficient Parallel Algorithms, Cambridge University Press, (1988).Google Scholar
  8. [8]
    R.M. Karp, V. Ramachandran, A survey of parallel algorithms for shared memory machines, Handbook of Theor. Comp. Sc., Ed. Van Leeuwen, North Holland (1992) pp 869–942.Google Scholar
  9. [9]
    S. Rao Kosaraju, A.L. Delcher, Optimal Parallel Evaluation of Tree-structured Computations by Raking, LNCS nℴ 319, VLSI Algorithms and Architectures, pp 103–110.Google Scholar
  10. [10]
    G.L. Millet, V. Ramachandran, E. Kaltofen, Efficient Parallel Evaluation of Straight-Line Code and Arithmetic Circuits, Proc. Aegean Workshop on Computing, LNCS nℴ 227, (1986), pp 236–251.Google Scholar
  11. [11]
    A. Gibbons, M. Patterson, Dense-Edgs Embedding of binary trees in the mesh, Proc. SPAA, (1992) pp 257–263.Google Scholar
  12. [12]
    M.S. Patterson, W.L. Ruzzo, L. Snyder, Bounds on Minimax Edge Length for Complete Binary Trees, Proc. of the 13th ACM Symp. on the Theory of Comp., (1981), pp 293–299.Google Scholar
  13. [13]
    C. Papadimitriou, J. Ullman, A Communication Time Tradeoff, SIAM J. on Computing, Vol. 16, No 4, (1987), pp 639–646.CrossRefGoogle Scholar
  14. [14]
    W.L. Ruzzo, L. Snyder, Minimum Edge Length Planar Embeddings of Trees, in Kung, Sprull, Steele: VLSI Systems and Computations, Comp. Sc. Press, 119–123(1981).Google Scholar
  15. [15]
    Y. Saad, Some Topological Properties of the Hypercube Multiprocessor, Research Report 389, Dept. Comp. Sc., Yale University (1984).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • E. Bampis
    • 1
    • 2
  • J. -C. König
    • 1
    • 2
  • D. Trystram
    • 3
  1. 1.LRI, Bât 490, Université de Paria SudOrsay CedexFrance
  2. 2.LIVE, Université d'EvryEvry CedexFrance
  3. 3.LMC-IMAGGrenoble CedexFrance

Personalised recommendations