Skip to main content

Divide-and-conquer algorithms on the hypercube

  • Conference paper
  • First Online:
STACS 93 (STACS 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 665))

Included in the following conference series:

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. 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. 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. 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. A. van Gelder. PRAM processor allocation: A hidden bottleneck in sublogarithmic algorithms IEEE Transactions on Computers, C-38:289–292, 1989.

    Google Scholar 

  5. 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. F.T. Leighton. Introduction to Parallel Algorithms and Architectures. Morgan Kaufmann Publishers, 1992.

    Google Scholar 

  7. 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. D. Nassimi and S. Sahni. Data broadcasting in SIMD computers. IEEE Transactions on Computers, C-30:101–107, 1981.

    Google Scholar 

  9. 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. D. Nassimi and S. Sahni. Parallel permutation and sorting algorithms and a new generalized connection network. JACM, 29:642–667, 1982.

    Google Scholar 

  11. 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. 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. J.T. Schwartz. Ultracomputers. ACM Transactions on Programming Languages and Systems, 2:484–521, 1980.

    Google Scholar 

  14. 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 

Download references

Author information

Authors and Affiliations

Authors

Editor information

P. Enjalbert A. Finkel K. W. Wagner

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Mayr, E.W., Werchner, R. (1993). Divide-and-conquer algorithms on the hypercube. In: Enjalbert, P., Finkel, A., Wagner, K.W. (eds) STACS 93. STACS 1993. Lecture Notes in Computer Science, vol 665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56503-5_18

Download citation

  • DOI: https://doi.org/10.1007/3-540-56503-5_18

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56503-1

  • Online ISBN: 978-3-540-47574-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics