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A time-space tradeoff for element distinctness

  • A. Borodin
  • F. Fich
  • F. Meyer auf der Heide
  • E. Upfal
  • A. Wigderson
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 210)

Abstract

In "A Time Space Tradeoff for Sorting on non-Oblivious Machines", Borodin et al. [B - 81] proved that to sort n elements requires TS = Ω(n2) where T=time and S=space on a comparison based branching problem. Although element distinctness and sorting are equivalent problems on a computation tree, the stated tradeoff result does not immediately follow for element distinctness or indeed for any decision problem. In this paper, we are able to show that TS=Ω(n3/2) for deciding element distinctness (or the sign of a permutation).

Keywords

Directed Acyclic Graph Computation Tree Main Lemma Adjacent Pair Arithmetic Circuit 
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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References

  1. [BC-82] Borodin A. and Cook S., A Time-Space Tradeoff for Sorting on a General Sequential Model of Computation, SICOMP 11(2), May 1982, pp. 287–297.Google Scholar
  2. [B-81] Borodin A., Fischer M., Kirkpatrick D., Lynch N., Tompa M., A Time-Space Tradeoff on Non-Oblivious Machines, J.C.S.S. 22(3), June 1981, pp.351–364.Google Scholar
  3. [C-66] Cobham A., The Recognition Problem for the Set of Perfect Squares, Research Paper RC-1704, IBM Watson Research Center, Yorktown Hights, N.Y., April 1966.Google Scholar
  4. [R-72] Reingold E., On the Optimality of some Set Algorithms, J. ACM 19, 1972, pp.649–659.CrossRefGoogle Scholar
  5. [T-80] Tompa M., Time-Space Tradeoffs for Computing Functions Using Connectivity Properties of their Circuits, J.C.S.S. 20(2), 1980, pp.118–132.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • A. Borodin
    • 1
  • F. Fich
    • 2
  • F. Meyer auf der Heide
    • 3
  • E. Upfal
    • 4
  • A. Wigderson
    • 5
  1. 1.University of TorontoTorontoCanada
  2. 2.University of WashingtonSeattle
  3. 3.Johann Wolfgang Goethe Universität Frankfurt a. M.Fed. Rep. of Germany
  4. 4.IBM Research LaboratorySan Jose
  5. 5.Mathematical Science Research InstituteBerkeley

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