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Fast deterministic selection on mesh-connected processor arrays

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Abstract

We present a deterministic algorithm for selecting the element of rankk amongN=n 2 elements, 1≤k≤N, on ann×n mesh-connected processor array in 1.45n parallel computation steps, using constant-sized queues (for large enoughn). This is a considerable improvement over the best previous deterministic algorithm, which was based upon sorting and requires2n+o(n) steps. Our algorithm can be generalized to solve the problem of selection on higher-dimensional meshes. In particular, we present an algorithm for the three-dimensional mesh which achieves a time bound better than any of the previously known deterministic results.

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References

  1. A. Agarwal, B. Lim, D. Kranz, and J. Kubiatowicz. APRIL: a processor architecture for multiprocessing.Proceedings of the 17th Annual International Symposium on Computer Architecture, pp. 104–114, 1990.

  2. M. Ajtai, N. Komlos, W. L. Steiger, and E. Szemeredi. Optimal parallel selection has complexityO(loglogn).Journal of Computer and System Science, 38(1):125–133, February 1989.

    Article  Google Scholar 

  3. Y. Azar and N. Pippenger. Parallel selection.Discrete Applied Mathematics, 27:49–58, 1990.

    Article  Google Scholar 

  4. M. Blum, R. Floyd, V. R. Pratt, R. Rivest, and R. Tarjan. Time bounds for selection.Journal of Computer and System Science, 7(4):448–461, 1972.

    Google Scholar 

  5. R. Cole. An optimally efficient selection algorithm.Information Processing Letters, 26:295–299, 1988.

    Article  MathSciNet  Google Scholar 

  6. A. Condon and L. Narayanan. Upper bounds for sorting and selection on meshes.Proceedings of the Sixth IEEE Symposium on Parallel and Distributed Processing, pp. 497–504, 1994.

  7. W. Dally. Wire efficient VLSI multi-processor communication networks. InAdvanced Research in VLSI, pp. 391–415. MIT Press, Cambridge, MA, 1987.

    Google Scholar 

  8. C. Kaklamanis, D. Krizanc, L. Narayanan, and A. Tsantilas. Randomized sorting and selection on meshconnected processor arrays.Proceedings of the Symposium on Parallel Algorithms and Architecture, pages 17–28, 1991.

  9. M. Kaufmann, J. Sibeyn, and T. Suel. Derandomizing algorithms for routing and sorting on meshes.Proceedings of the Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 669–679, 1994.

  10. M. Kunde. Routing and sorting on mesh-connected arrays. InAegean Workshop on Computing: VLSI Algorithms and Architectures, pp. 423–433. Lecture Notes in Computer Science, Vol. 319. Springer-Verlag, Berlin, 1988.

    Google Scholar 

  11. M. Kunde. 1-selection and related problems on grids of processors.Journal of New Generation Computer Systems, 2:129–143, 1989.

    Google Scholar 

  12. M. Kunde. Concentrated regular data streams on grids: sorting and routing near to the bisection bound.Proceedings of the Symposium on the Foundations of Computer Science, pp. 141–150, 1991.

  13. F. Leighton, F. Makedon, and I. Tollis. A 2n−2 step algorithm for routing in ann×n array with constant size queues.Proceedings of the Symposium on Parallel Algorithms and Architecture, pp. 328–335, 1989.

  14. D. Lenoski, J. Laudon, K. Gharachorloo, A. Gupta, and J. Hennessy. The directory-based cache coherence protocol for the DASH multiprocessor.Proceedings of the 17th Annual International Symposium on Computer Architecture, pp. 148–159, 1990.

  15. S. L. Lillevik. Touchstone program overview.Proceedings of the 5th Distributed Memory Computing Conference, Charleston, SC, April 9–12, 1990.

  16. F. Makedon and A. Simvonis. Many-to-one packet routing for the mesh. Technical Report, University of Texas at Dallas., 1991.

    Google Scholar 

  17. G. Plaxton. Load balancing, selection and sorting on the hypercube.Proceedings of the Symposium on Parallel Algorithms and Architecture, pp. 64–73, 1989.

  18. G. Plaxton. On the network complexity of selection.Proceedings of the Symposium on the Foundations of Computer Science, pp. 396–401, 1989.

  19. S. Rajasekaran. Randomized parallel selection. InFoundations of Software Technology and Theoretical Computer Science, pp. 176–184. Lecture Notes in Computer Science, Vol. 472. Springer-Verlag, Berlin, 1990.

    Google Scholar 

  20. S. Rajasekaran and T. Tsantilas. Optimal algorithms for routing on the mesh.Algorithmica, 8:21–38, 1992.

    MathSciNet  Google Scholar 

  21. R. Reischuk. Probabilistic parallel algorithms for sorting and selection.SIAM Journal of Computing, 14(2):396–411, May 1985.

    Article  Google Scholar 

  22. C. Schnorr and A. Shamir. An optimal sorting algorithm for mesh-connected computers.Proceedings of the Symposium on the Theory of Computation, pp. 255–263, 1986.

  23. C. Thompson and H. Kung. Sorting on a mesh connected parallel computer.Communications of the ACM, 20:263–270, 1977.

    Article  Google Scholar 

  24. L. Valiant. Parallelism in comparison problems.SIAM Journal of Computing, 4:348–355, 1975.

    Article  Google Scholar 

  25. U. Vishkin. An optimal parallel algorithm for selection. InAdvances in Computing Research, pp. 79–85. JAI Press, Greenwich, CT, 1987.

    Google Scholar 

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Authors and Affiliations

  1. School of Computer Science, Carleton University, K1S 5B6, Ottawa, Ontario, Canada

    D. Krizanc

  2. Department of Computer Science, Concordia University, H3G 1M8, Montreal, Quebec, Canada

    L. Narayanan

  3. Department of Computer Science, King's College London, WC2R 2LS, Strand, London, England

    R. Raman

Authors
  1. D. Krizanc
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  2. L. Narayanan
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  3. R. Raman
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Additional information

Communicated by N. Megiddo.

This research was done while all three authors were at the University of Rochester, New York.

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Krizanc, D., Narayanan, L. & Raman, R. Fast deterministic selection on mesh-connected processor arrays. Algorithmica 15, 319–331 (1996). https://doi.org/10.1007/BF01961542

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  • DOI: https://doi.org/10.1007/BF01961542

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