Skip to main content

A Simple Optimal Randomized Algorithm for Sorting on the PDM

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3827))

Abstract

The Parallel Disks Model (PDM) has been proposed to alleviate the I/O bottleneck that arises in the processing of massive data sets. Sorting has been extensively studied on the PDM model due to the fundamental nature of the problem. Several randomized algorithms are known for sorting. Most of the prior algorithms suffer from undue complications in memory layouts, implementation, or lack of tight analysis. In this paper we present a simple randomized algorithm that sorts in optimal time with high probablity and has all the desirable features for practical implementation.

This research been supported in part by the NSF Grants CCR-9912395 and ITR-0326155.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aggarwal, A., Plaxton, G.: Optimal parallel sorting in multi-level storage. In: Proc of the ACM-SIAM SODA 1994, pp. 659–668 (1994)

    Google Scholar 

  2. Aggarwal, A., Vitter, J.S.: The Input/Output Complexity of Sorting and Related Problems. Communications of the ACM 31(9), 1116–1127 (1988)

    Article  MathSciNet  Google Scholar 

  3. Arge, L.: The Buffer Tree: A New Technique for Optimal I/O-Algorithms. In: Sack, J.-R., Akl, S.G., Dehne, F., Santoro, N. (eds.) WADS 1995. LNCS, vol. 955, pp. 334–345. Springer, Heidelberg (1995)

    Google Scholar 

  4. Arge, L., Ferragina, P., Grossi, R., Vitter, J.S.: On Sorting Strings in External Memory. In: Proc. ACM Symposium on Theory of Computing (1995)

    Google Scholar 

  5. Arge, L., Knudsen, M., Larsen, K.: A General Lower Bound on the I/O-Complexity of Comparison-based Algorithms. In: Dehne, F., Sack, J.-R., Santoro, N. (eds.) WADS 1993. LNCS, vol. 709. Springer, Heidelberg (1993)

    Google Scholar 

  6. Barve, R., Grove, E.F., Vitter, J.S.: Simple Randomized Mergesort on Parallel Disks. Parallel Computing 23(4-5), 601–631 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  7. Batcher, K.: Sorting Networks and their Applications. In: Proc. AFIPS Spring Joint Computing Conference, vol. 32, pp. 307–314 (1968)

    Google Scholar 

  8. Chaudhry, G., Cormen, T.H.: Getting More From Out-of-Core Columnsort. In: Mount, D.M., Stein, C. (eds.) ALENEX 2002. LNCS, vol. 2409, pp. 143–154. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  9. Chaudhry, G., Cormen, T.H., Hamon, E.A.: Parallel Out-of-Core Sorting: The Third Way. To appear in Cluster Computing

    Google Scholar 

  10. Chaudhry, G., Cormen, T.H., Wisniewski, L.F.: Columnsort Lives! An Efficient Out-of-Core Sorting Program. In: Proc. 13th Annual ACM Symposium on Parallel Algorithms and Architectures, pp. 169–178 (2001)

    Google Scholar 

  11. Dementiev, R., Sanders, P.: Asynchronous Parallel Disk Sorting. In: Proc. ACM Symposium on Parallel Algorithms and Architectures, pp. 138–148 (2003)

    Google Scholar 

  12. Horowitz, E., Sahni, S., Rajasekaran, S.: Computer Algorithms. W.H. Freeman, New York (1998)

    Google Scholar 

  13. Hutchinson, D., Sanders, P., Vitter, J.: Duality between prefetching and queued writing with parallel disks. In: Meyer auf der Heide, F. (ed.) ESA 2001. LNCS, vol. 2161, pp. 62–73. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  14. Leighton, T.: Tight Bounds on the Complexity of Parallel Sorting. IEEE Transactions on Computers C34(4), 344–354 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  15. Nodine, M., Vitter, J.: Deterministic distribution sort in shared and distributed memory multirocessors. In: Proc. of the ACM SPAA 1993, pp. 120–129 (1993)

    Google Scholar 

  16. Nodine, M.H., Vitter, J.S.: Greed Sort: Optimal Deterministic Sorting on Parallel Disks. Journal of the ACM 42(4), 919–933 (1995)

    Article  MathSciNet  Google Scholar 

  17. Rajasekaran, S.: Sorting and selection on interconnection networks. DIMACS Series in Discrete Mathematics and Theoretical Computer Science 21, pp. 275–296 (1995)

    Google Scholar 

  18. Rajasekaran, S.: A Framework for Simple Sorting Algorithms on Parallel Disk Systems. Theory of Computing Systems 34(2), 101–114 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  19. Rajasekaran, S., Sen, S.: PDM Sorting Algorithms That Take A Small Number of Passes (manuscript 2004)

    Google Scholar 

  20. Sanders, P., Enger, S., Korst, J.: Fast concurrent access to parallel disks. In: Proc. of the ACM-SIAM SODA 2000, pp. 849–858 (2000)

    Google Scholar 

  21. Thompson, C.D., Kung, H.T.: Sorting on a Mesh Connected Parallel Computer. Communications of the ACM 20(4), 263–271 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  22. Vitter, J.S., Hutchinson, D.A.: Distribution Sort with Randomized Cycling. In: Proc. 12th Annual SIAM/ACM Symposium on Discrete Algorithms (2001)

    Google Scholar 

  23. Vitter, J.S., Shriver, E.A.M.: Algorithms for Parallel Memory I: Two-Level Memories. Algorithmica 12(2-3), 110–147 (1994)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Rajasekaran, S., Sen, S. (2005). A Simple Optimal Randomized Algorithm for Sorting on the PDM. In: Deng, X., Du, DZ. (eds) Algorithms and Computation. ISAAC 2005. Lecture Notes in Computer Science, vol 3827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11602613_55

Download citation

  • DOI: https://doi.org/10.1007/11602613_55

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30935-2

  • Online ISBN: 978-3-540-32426-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics