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Fast Periodic Correction Networks

  • Grzegorz Stachowiak
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2751)

Abstract

We consider the problem of sorting N-element inputs differing from already sorted sequences on t entries. To perform this task we construct a comparator network that is applied periodically. The two constructions for this problem made by previous authors required O(log n + t) iterations of the network. Our construction requires O(log n + (log log N)2 (log t)3) iterations which makes it faster for t ≫ log N.

Keywords

sorting network comparator periodic sorting network 

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References

  1. 1.
    Ajtai, M., Komolós, J., Szemerédi, E.: Sorting in c log n parallel steps. Combinatorica 3, 1–19 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Batcher, K.E.: Sorting networks and their applications. In: AFIPS Conf. Proc., vol. 32, pp. 307–314 (1968)Google Scholar
  3. 3.
    Dowd, M., Perl, Y., Saks, M., Rudolph, L.: The Periodic Balanced Sorting Network. Journal of the ACM 36, 738–757 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Kik, M., Kutyłowski, M., Piotrów, M.: Correction Networks. In: Proc. of 1999 ICPP, pp. 40–47 (1999)Google Scholar
  5. 5.
    Kik, M., Kutyłowski, M., Stachowiak, G.: Periodic constant depth sorting networks. In: Proc. of the 11th STACS, pp. 201–212 (1994)Google Scholar
  6. 6.
    Kik, M.: Periodic Correction Networks. In: Bode, A., Ludwig, T., Karl, W.C., Wismüller, R. (eds.) Euro-Par 2000. LNCS, vol. 1900, pp. 471–478. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  7. 7.
    Knuth, D.E.: The Art of Computer Programming, 2nd edn., vol. 3. AddisonWesley, Reading (1975)Google Scholar
  8. 8.
    Krammer, J.: Lösung von Datentransportproblemen in integrierten Schaltungen. Dissertation, TU München (1991)Google Scholar
  9. 9.
    Loryś, K., Kutyłowski, M., Oesterdiekoff, B., Wanka, R.: Fast and Feasible Periodic Sorting Networks of Constant Depth. In: Proc of 35 IEEE-FOCS, pp. 369–380 (1994)Google Scholar
  10. 10.
    Oesterdiekoff, B.: On the Minimal Period of Fast Periodic Sorting Networks, Technical Report TR-RI-95-167, University of Paderborn (1995)Google Scholar
  11. 11.
    Piotrów, M.: Depth Optimal Sorting Networks Resistant to k Passive Faults. In: Proc. 7th SIAM Symposium on Discrete Algorithms, pp. 242–251 (1996); (also accepted for SIAM J. Comput.)Google Scholar
  12. 12.
    Piotrów, M.: Periodic Random-Fault-Tolerant Correction Networks. In: Proceedings of 13th SPAA, pp. 298–305. ACM Press, New York (2001)Google Scholar
  13. 13.
    Rudolph, L.: ARobust Sorting Network. IEEETransactions on Computers 34, 326–336 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Schimmler, M., Starke, C.: A Correction Network for N-Sorters. SIAM J. Comput. 18, 1179–1197 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Schwiegelsohn, U.: A shortperiodic two-dimensional systolic sorting algorithm. In: International Conference on Systolic Arrays, pp. 257–264. Computer Society Press, Baltimore (1988)CrossRefGoogle Scholar
  16. 16.
    Stachowiak, G.: Fibonacci Correction Networks. In: Halldórsson, M.M. (ed.) SWAT 2000. LNCS, vol. 1851, pp. 535–548. Springer, Heidelberg (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Grzegorz Stachowiak
    • 1
  1. 1.Institute of Computer ScienceUniversity of WrocławWrocławPoland

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