A lower bound for the complexity of the Union-Split-Find problem

  • K. Mehlhorn
  • S. Näher
  • H. Alt
Algorithms And Complexity
Part of the Lecture Notes in Computer Science book series (LNCS, volume 267)


We prove a Θ(log log n) (i.e. matching upper and lower) bound on the complexity of the Union-Split-Find problem, a variant of the Union-Find problem. Our lower bound holds for all pointer machine algorithms and does not require the separation assumption used in the lower bound arguments of Tarjan [T79] and Blum [B86]. We complement this with a Θ(log n) bound for the Split-Find problem under the separation assumption. This shows that the separation assumption can imply an exponential loss in efficiency.


Output Node Input Node Split Operation Output Record Separation Assumption 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • K. Mehlhorn
    • 1
  • S. Näher
    • 1
  • H. Alt
    • 2
  1. 1.FB10, InformatikUniversität des SaarlandesSaarbrückenWest-Germany
  2. 2.FB Mathematik, WE 3Freie Universität BerlinBerlin 33West-Germany

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