Skip to main content
SpringerLink
Log in

PRAM lower bound for element distinctness revisited

  • Contributed Papers
  • Conference paper
  • First Online:
SOFSEM'97: Theory and Practice of Informatics (SOFSEM 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1338))

  • 136 Accesses

Abstract

This paper considers the problem of element distinctness on CRCW PRAMS with unbounded memory. A complete proof of the optimal lower bound of Ω (n log n/(p log(n/p log n + 1)) ) steps for n elements problem on p processor COMMON PRAM is presented. This lower bound has been previously correctly stated by Boppana, but his proof was not complete. Its correction requires some additional observations and some not straightforward changes.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Boppana R.V.: Optimal Separations Between Concurrent-Write Parallel Machines, Proc. 21th ACM Symp. on Theory of Computing (1989) 320–326

    Google Scholar 

  2. Chernof H.: A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the Sum of Observations, Annals of Math. Stat. 23 (1952) 493–509

    Google Scholar 

  3. Edmonds J.: Lower Bounds with Smaller Domain Size, Structures in Complexity Theory (1991) 322–331

    Google Scholar 

  4. Edmonds J.: Removing Ramsey Theory: Lower Bounds with Smaller Domain Size, Journal of Theoretic Computer Science, submited, available as Postscript file at http://www.cs.yorku.ca/~jeff/research/ index. html

    Google Scholar 

  5. Erdös P. and Rado R.: A Combinatorial Theorem, J. London Math. Soc. 25 (1950) 376–382

    Google Scholar 

  6. Fredman M., Komlós J.: On the Size of Separating Systems and Families of Perfect Hash Functions, SIAM J. Alg. Disc. Meth. 5 (1984) 61–68

    Google Scholar 

  7. Fich F. E., Meyer Auf Der Heide F., Wigderson A.: Lower Bounds for Parallel Random-Access Machines with Unbounded Shared Memory, Advances in Computing Research 4 (1986) 1–15

    Google Scholar 

  8. Fich, F. E., Ragde, P. L., Wigderson, A.: Relations Between Concurrent-Write Models of Parallel Computation, SIAM J. Comp. 17 (1988) 606–627

    Google Scholar 

  9. Kolman, P.: Complexity of Some Problems on COMMON PRAM, Masters Thesis, Charles University, Prague (1995), in Czech

    Google Scholar 

  10. Meyer Auf Der Heide F., Wigderson A.: The Comlexity of Parallel Sorting, 26th FOGS (1985) 532–540

    Google Scholar 

  11. Ragde P. L., Steiger W., Szemeredi E., Wigderson A.: The Parallel Complexity of Element Distinctness is \(\Omega \left( {\sqrt {\log {\text{ }}n} } \right)\), SIAM J. Disc. Math. 1 (1988) 399–410

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic

    Petr Kolman

Authors
  1. Petr Kolman
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

František Plášil Keith G. Jeffery

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kolman, P. (1997). PRAM lower bound for element distinctness revisited. In: Plášil, F., Jeffery, K.G. (eds) SOFSEM'97: Theory and Practice of Informatics. SOFSEM 1997. Lecture Notes in Computer Science, vol 1338. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63774-5_125

Download citation

  • DOI: https://doi.org/10.1007/3-540-63774-5_125

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63774-5

  • Online ISBN: 978-3-540-69645-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation