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]:
$$ \begin{aligned} N &= \mathrm{problem\ size\ (in\ units\ of\ data\ items)\:;} \\ M &= \mathrm{internal\ memory\ size\ (in\ units\ of\ data\ items)\:;} \\ B &= \mathrm{block\ transfer\ size\ (in\ units\ of\ data\ items)\:;} \\ D &= \mathrm{number\ of\ independent\ disk\ drives\:;}\\ P &= \mathrm{number\ of\ CPUs\:,} \end{aligned} $$

Keywords

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
  2. 2.
    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
  3. 3.
    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
  4. 4.
    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
  5. 5.
    Barve, R.D., Vitter, J.S.: A simple and efficient parallel disk mergesort. ACM Trans. Comput. Syst. 35, 189–215 (2002)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Cormen, T.H., Sundquist, T., Wisniewski, L.F.: Asymptotically tight bounds for performing BMMC permutations on parallel disk systems. SIAM J. Comput. 28, 105–136 (1999)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Hutchinson, D.A., Sanders, P., Vitter, J.S.: Duality between prefetching and queued writing with parallel disks. SIAM J. Comput. 34, 1443–1463 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Kallahalla, M., Varman, P.J.: Optimal read-once parallel disk scheduling. Algorithmica 43, 309–343 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Knuth, D.E.: Sorting and Searching. The Art of Computer Programming, vol. 3, 2nd edn. Addison-Wesley, Reading (1998)Google Scholar
  10. 10.
    Matias, Y., Segal, E., Vitter, J.S.: Efficient bundle sorting. SIAM J. Comput. 36(2), 394–410 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    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
  12. 12.
    Nodine, M.H., Vitter, J.S.: Greed Sort: An optimal sorting algorithm for multiple disks. J. ACM 42, 919–933 (1995)MathSciNetCrossRefGoogle Scholar
  13. 13.
    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
  14. 14.
    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
  15. 15.
    Vitter, J.S., Hutchinson, D.A.: Distribution sort with randomized cycling. J. ACM. 53 (2006)Google Scholar
  16. 16.
    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