Divide-and-conquer algorithms on the hypercube

  • Ernst W. Mayr
  • Ralph Werchner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 665)


We show how to implement divide-and-conquer algorithms without undue overhead on a wide class of networks. We give an optimal generic divide-and-conquer implementation on hypercubes for the class of divide-and-conquer algorithms for which the total size of the subproblems on any level of the recursion does not exceed the parent problem size. For this implementation, appropriately sized subcubes have to be allocated to the subproblems generated by the divide-steps. We take care that these allocation steps do not cause any unbalanced distribution of work, and that, asymptotically, they do not increase the running time. Variants of our generic algorithm also work for the butterfly network and, by a general simulation, for the class of hypercubic networks, including the shuffle-exchange and the cube-connected-cycles network. Our results can also be applied to optimally solve various types of routing problems.


Theory of Parallel and Distributed Computation Algorithms and Data Structures 


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  1. [CL90]
    M.Y. Chan and S.-J. Lee. Subcube recognition, allocation/deallocation and relocation in hypercubes. Proceedings of the 2nd IEEE Symposium on Parallel and Distributed Processing, 87–93, 1990.Google Scholar
  2. [CS87]
    M.-S. Chen and K.G. Shin. Processor allocation in an N-cube multiprocessor using Gray codes. IEEE Transactions on Computers, C-36:1396–1407, 1987.Google Scholar
  3. [FW78]
    S. Fortune and J. Wyllie. Parallelism in random access machines. Proceedings of the 10th ACM Symposium on Theory of Computing, 114–118, 1978.Google Scholar
  4. [vG89]
    A. van Gelder. PRAM processor allocation: A hidden bottleneck in sublogarithmic algorithms IEEE Transactions on Computers, C-38:289–292, 1989.Google Scholar
  5. [KDL89]
    J. Kim and C.R. Das and W. Lin. A processor allocation scheme for hypercube computers. Proceedings of the 1989 International Conference on Parallel Processing. Vol. 2 Software, 231–238, 1989.Google Scholar
  6. [L92]
    F.T. Leighton. Introduction to Parallel Algorithms and Architectures. Morgan Kaufmann Publishers, 1992.Google Scholar
  7. [MW92]
    E.W. Mayr and R. Werchner. Optimal routing of parentheses on the hypercube. Proceedings of the 4th Annual ACM Symposium on Parallel Algorithms and Architectures, 109–117, 1992.Google Scholar
  8. [NS81]
    D. Nassimi and S. Sahni. Data broadcasting in SIMD computers. IEEE Transactions on Computers, C-30:101–107, 1981.Google Scholar
  9. [NS82a]
    D. Nassimi and S. Sahni. A self-routing Benes network and parallel permutation algorithms. IEEE Transactions on Computers, C-31:148–154, 1982.Google Scholar
  10. [NS82b]
    D. Nassimi and S. Sahni. Parallel permutation and sorting algorithms and a new generalized connection network. JACM, 29:642–667, 1982.Google Scholar
  11. [PM89]
    C.G. Plaxton and E.W. Mayr. Pipelined parallel prefix computations and sorting on a pipelined hypercube. Technical Report STAN-CS-89-1269, Stanford University, 1989. To appear in J. Parallel Distrib. Comput.Google Scholar
  12. [S90]
    E.J. Schwabe. On the computational equivalence of hypercube-derived networks. Proceedings of the 2nd Annual ACM Symposium on Parallel Algorithms and Architectures, 388–397, 1990.Google Scholar
  13. [S80]
    J.T. Schwartz. Ultracomputers. ACM Transactions on Programming Languages and Systems, 2:484–521, 1980.Google Scholar
  14. [ZRL91]
    X. Zhong, S. Rajopadhye and V.M. Lo. Parallel implementations of divide-and-conquer algorithms on binary de Bruijn networks. Technical Report CIS-TR-91-21 University of Oregon, 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Ernst W. Mayr
    • 1
  • Ralph Werchner
    • 1
  1. 1.Fachbereich InformatikJ.W. Goethe-UniversityFrankfurt am MainGermany

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