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)


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).


Directed Acyclic Graph Computation Tree Main Lemma Adjacent Pair Arithmetic Circuit 
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  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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