Encyclopedia of Algorithms

2008 Edition
| Editors: Ming-Yang Kao

External Sorting and Permuting

1988; Aggarwal, Vitter
  • Jeffrey Scott Vitter
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30162-4_137

Keywords and Synonyms

Out-of-core sorting              

Problem Definition

Notations The main properties of magnetic disks and multiple disk systems can be captured by the commonly used parallel disk model (PDM), which is summarized below in its current form as developed by Vitter and Shriver [ 16]:
$$ \begin{aligned} N &= \mathrm{problem\ size\ (in\ units\ of\ data\ items)\:;} \\ M &= \mathrm{internal\ memory\ size\ (in\ units\ of\ data\ items)\:;} \\ B &= \mathrm{block\ transfer\ size\ (in\ units\ of\ data\ items)\:;} \\ D &= \mathrm{number\ of\ independent\ disk\ drives\:;}\\ P &= \mathrm{number\ of\ CPUs\:,} \end{aligned} $$


Data Item Internal Memory Read Operation Matrix Transposition Realizable Ordering 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Recommended Reading

  1. 1.
    Aggarwal, A., Plaxton, C.G.: Optimal parallel sorting in multi-level storage. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, vol. 5, pp. 659–668. ACM Press, New York (1994)Google Scholar
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    Aggarwal, A., Vitter, J.S.: The Input/Output complexity of sorting and related problems. In: Communications of the ACM, 31 (1988), pp. 1116–1127. ACM Press, New York (1988)Google Scholar
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    Arge, L., Knudsen, M., Larsen, K.: A general lower bound on the I/O-complexity of comparison-based algorithms. In: Proceedings of the Workshop on Algorithms and Data Structures. Lect. Notes Comput. Sci. 709, 83–94 (1993)Google Scholar
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    Barve, R.D., Kallahalla, M., Varman, P.J., Vitter, J.S.: Competitive analysis of buffer management algorithms. J. Algorithms 36, 152–181 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
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    Barve, R.D., Vitter, J.S.: A simple and efficient parallel disk mergesort. ACM Trans. Comput. Syst. 35, 189–215 (2002)MathSciNetzbMATHGoogle Scholar
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    Kallahalla, M., Varman, P.J.: Optimal read-once parallel disk scheduling. Algorithmica 43, 309–343 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
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    Knuth, D.E.: Sorting and Searching. The Art of Computer Programming, vol. 3, 2nd edn. Addison-Wesley, Reading (1998)Google Scholar
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    Matias, Y., Segal, E., Vitter, J.S.: Efficient bundle sorting. SIAM J. Comput. 36(2), 394–410 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
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    Nodine, M.H., Vitter, J.S.: Deterministic distribution sort in shared and distributed memory multiprocessors. In: Proceedings of the ACM Symposium on Parallel Algorithms and Architectures, June–July 1993, vol. 5, pp. 120–129, ACM Press, New York (1993)Google Scholar
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    Nodine, M.H., Vitter, J.S.: Greed Sort: An optimal sorting algorithm for multiple disks. J. ACM 42, 919–933 (1995)MathSciNetCrossRefGoogle Scholar
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    Shah, R., Varman, P.J., Vitter, J.S.: Online algorithms for prefetching and caching on parallel disks. In: Proceedings of the ACM Symposium on Parallel Algorithms and Architectures, pp. 255–264. ACM Press, New York (2004)Google Scholar
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    Vitter, J.S.: External memory algorithms and data structures: Dealing with Massive Data. ACM Comput. Surv. 33(2), 209–271 (2001) Revised version available at http://www.cs.purdue.edu/homes/jsv/Papers/Vit.IO_survey.pdf CrossRefGoogle Scholar
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    Vitter, J.S., Hutchinson, D.A.: Distribution sort with randomized cycling. J. ACM. 53 (2006)Google Scholar
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    Vitter, J.S., Shriver, E.A.M.: Algorithms for parallel memory I: Two-level memories. Algorithmica 12, 110–147 (1994)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Jeffrey Scott Vitter
    • 1
  1. 1.Department of Computer SciencePurdue UniversityWest LafayetteUSA