Efficient Parallel Tree Reductions on Distributed Memory Environments

  • Kazuhiko Kakehi
  • Kiminori Matsuzaki
  • Kento Emoto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4488)


A new approach for fast parallel reductions on trees over distributed memory environments is proposed. By employing serialized trees as the data representation, our algorithm has a communication-efficient BSP implementation regardless of the shapes of inputs. The prototype implementation supports its real efficacy.


Tree reduction parentheses matching BSP parallel algorithm 


  1. 1.
    Berkman, O., Schieber, B., Vishkin, U.: Optimal doubly logarithmic parallel algorithms based on finding all nearest smaller values. Journal of Algorithms 14 (1993)Google Scholar
  2. 2.
    Prasad, S., Das, S., Chen, C.: Efficient EREW PRAM algorithms for parentheses-matching. IEEE Transactions on Parallel and Distributed Systems 5(9) (1994)Google Scholar
  3. 3.
    Cole, M.: Parallel programming with list homomorphisms. Parallel Processing Letters 5 (1995)Google Scholar
  4. 4.
    Kravets, D., Plaxton, C.: All nearest smaller values on the hypercube. IEEE Transactions on Parallel and Distributed Systems 7(5) (1996)Google Scholar
  5. 5.
    He, X., Huang, C.: Communication efficient BSP algorithm for all nearest smaller values problem. Journal of Parallel and Distributed Computing 16 (2001)Google Scholar
  6. 6.
    Valiant, L.: A bridging model for parallel computation. Communication of the ACM 33(8) (1990)Google Scholar
  7. 7.
    Kakehi, K., Matsuzaki, K., Emoto, K., Hu, Z.: A practicable framework for tree reduction under distributed memory environments. Technical Report METR 2006-64, Department of Mathematical Informatics, University of Tokyo (2006)Google Scholar
  8. 8.
    Skillicorn, D.B.: Parallel implementation of tree skeletons. Journal of Parallel and Distributed Computing 39(2) (1996)Google Scholar
  9. 9.
    Matsuzaki, K., Hu, Z., Kakehi, K., Takeichi, M.: Systematic derivation of tree contraction algorithms. Parallel Processing Letters 15(3) (2005), Original version appeared in Proc. 4th International Workshop on Constructive Methodology of Parallel Programming (2004)Google Scholar
  10. 10.
    Mignet, L., Barbosa, D., Veltri, P.: The XML web: a fist study. In: Proceedings of the Twelfth International World Wide Web Conference, ACM Press, New York (2003)Google Scholar
  11. 11.
    Mayr, E.W., Werchner, R.: Optimal routing of parentheses on the hypercube. Journal of Parallel and Distributed Computing 26(2) (1995)Google Scholar
  12. 12.
    Mayr, E.W., Werchner, R.: Optimal tree contraction and term matching on the hypercube and related networks. Algorithmica 18(3) (1997)Google Scholar
  13. 13.
    Dehne, F., Ferreira, A., Cáceres, E., Song, S., Roncato, A.: Efficient parallel graph algorithms for coarse-grained multicomputers and BSP. Algorithmica 33(2) (2002)Google Scholar
  14. 14.
    Reid-Miller, M., Miller, G.L., Modugno, F.: List ranking and parallel tree contraction. In: Reif, J.H. (ed.) Synthesis of Parallel Algorithms, Morgan Kaufmann, San Francisco (1993)Google Scholar
  15. 15.
    SkeTo Project Home Page,
  16. 16.
    Matsuzaki, K., Emoto, K., Iwasaki, H., Hu, Z.: A library of constructive skeletons for sequential style of parallel programming (invited paper). In: Proceedings of the First International Conference on Scalable Information Systems, IEEE Computer Society Press, Los Alamitos (2006)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Kazuhiko Kakehi
    • 1
  • Kiminori Matsuzaki
    • 2
  • Kento Emoto
    • 3
  1. 1.Division of University Corporate Relations 
  2. 2.Department of Mathematical Informatics 
  3. 3.Department of Creative Informatics, University of Tokyo 

Personalised recommendations