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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7285))

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Abstract

We present a more efficient CREW PRAM algorithm for integer sorting. This algorithm sorts n integers in { 0, 1, 2, ..., n 1/2} in O((logn)3/2/loglogn) time and O(n (logn/loglogn)1/2) operations. It also sorts n integers in {0, 1, 2,..., nā€‰āˆ’ā€‰1} in O((logn)3/2/loglogn) time and O(n (logn/loglogn)1/2logloglogn) operations. Previous best algorithm [13] on both cases has time complexity O(logn) but operation complexity O(n(logn)1/2).

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References

  1. Ajtia, M., KomlĆ³s, J., SzemerĆ©di, E.: Sorting in c logn parallel steps. CombinatoricaĀ 3, 1ā€“19 (1983)

    ArticleĀ  MathSciNetĀ  Google ScholarĀ 

  2. Albers, S., Hagerup, T.: Improved parallel integer sorting without concurrent writing. Information and ComputationĀ 136, 25ā€“51 (1997)

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  3. Andersson, A., Hagerup, T., Nilsson, S., Raman, R.: Sorting in linear time? In: Proc. 1995 Symposium on Theory of Computing, pp. 427ā€“436 (1995)

    Google ScholarĀ 

  4. Benes, V.E.: On rearrangeable three-stage connecting networks. Bell Syst. Tech. J.Ā 41, 1481ā€“1492 (1962)

    Google ScholarĀ 

  5. Benes, V.E.: Mathematical Theory of Connecting Networks and Telephone Traffic. Academic, New York (1965)

    MATHĀ  Google ScholarĀ 

  6. Chen, S., Reif, J.H.: Using difficulty of prediction to decrease computation: fast sort, priority queue and convex hull on entropy bounded inputs. In: 34th Annual IEEE Conference on Foundations of Computer Science (FOCS 1993) Proceedings, Palo Alto, CA, pp. 104ā€“112 (November 1993)

    Google ScholarĀ 

  7. Cook, S., Dwork, C., Reischuk, R.: Upper and Lower Time Bounds for Parallel Random Access Machines without Simultaneous Writes. SIAM J. Comput.Ā 15(1), 87ā€“97 (1986)

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  8. Goldberg, A.V., Plotkin, S.A., Shannon, G.E.: Parallel symmetry-breaking in sparse graphs. SIAM J. on Discrete Math.Ā 1(4), 447ā€“471 (1988)

    ArticleĀ  MathSciNetĀ  Google ScholarĀ 

  9. Han, Y.: Matching partition a linked list and its optimization. In: Proc. 1989 ACM Symposium on Parallel Algorithms and Architectures (SPAA 1989), Santa Fe, Mexico, pp. 246ā€“253 (June 1989)

    Google ScholarĀ 

  10. Han, Y.: An optimal linked list prefix algorithm on a local memory computer. In: Proc. 1989 Computer Science Conference (CSC 1989), pp. 278ā€“286 (February 1989)

    Google ScholarĀ 

  11. Han, Y.: Improved fast integer sorting in linear space. Information and ComputationĀ 170(1), 81ā€“94 (2001)

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  12. Han, Y.: Deterministic sorting in O(n loglogn) time and linear space. Journal of AlgorithmsĀ 50, 96ā€“105 (2004)

    ArticleĀ  MATHĀ  Google ScholarĀ 

  13. Han, Y., Shen, X.: Parallel integer sorting is more efficient than parallel comparison sorting on exclusive write PRAMs. SIAM J. Comput.Ā 31(6), 1852ā€“1878 (2002)

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  14. Hightower, W.L., Prins, J., Reif, J.H.: Implementations of randomized sorting on large parallel machines. In: 4th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA 1992), San Diego, CA, pp. 158ā€“167 (July 1992)

    Google ScholarĀ 

  15. JƔJƔ, J.: An Introduction to Parallel Algorithms. Addison-Wesley (1992)

    Google ScholarĀ 

  16. Leighton, T.: Tight bounds on the complexity of parallel sorting. IEEE Trans. Comput.Ā C-34, 344ā€“354 (1985)

    ArticleĀ  MathSciNetĀ  Google ScholarĀ 

  17. Reif, J.H.: An n 1ā€‰+ā€‰Īµ processor, O(logn) time probabilistic sorting algorithm. In: SIAM 2nd Conference on the Applications of Discrete Mathematics, Cambridge, MA, pp. 27ā€“29 (June 1983)

    Google ScholarĀ 

  18. Rajasekaran, S., Reif, J.H.: An optimal parallel algorithm for integer sorting. In: 26th Annual IEEE Symposium on Foundations of Computer Science, Portland, OR, pp. 496ā€“503 (October 1985); Published as Optimal and sublogarithmic time randomized parallel sorting algorithms. SIAM Journal on Computing 18(3), 594ā€“607 (1989)

    Google ScholarĀ 

  19. Valiant, L.G., Reif, J.H.: A Logarithmic Time Sort for Linear Size Networks. In: 15th Annual ACM Symposium on Theory of Computing, Boston, MA, pp. 10ā€“16 (April 1983); Published in Journal of the ACM(JACM) 34(1), 60ā€“76 (1987)

    Google ScholarĀ 

  20. Wyllie, J.C.: The complexity of parallel computation, TR 79-387, Department of Computer Science, Cornell University, Ithaca, NY (1979)

    Google ScholarĀ 

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Han, Y., He, X. (2012). More Efficient Parallel Integer Sorting. In: Snoeyink, J., Lu, P., Su, K., Wang, L. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 7285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29700-7_26

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  • DOI: https://doi.org/10.1007/978-3-642-29700-7_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29699-4

  • Online ISBN: 978-3-642-29700-7

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