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On the single-operation worst-case time complexity of the disjoint set union problem

  • Norbert Blum
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 182)

Abstract

We give an algorithm for the disjoint set union problem, within the class of algorithms defined by Tarjan, which has O(log n/loglog n) single-operation time complexity in the worst-case. Also we define a class of algorithms for the disjoint set union problem, which includes the class of algorithms defined by Tarjan. We prove that any algorithm from this class has at least ω(log n/loglog n) single-operation time complexity in the worst-case.

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References

  1. [M]
    Mehlhorn, K.: Data structures and algorithms 1, Sorting and Searching, Springer-Verlag (1984)Google Scholar
  2. [T1]
    Tarjan, R.E.: Efficiency of a good but not linear set union algorithm, JACM 22, 215–225 (1975)Google Scholar
  3. [T2]
    Tarjan, R.E.: A class of algorithms which require nonlinear time to maintain disjoint sets, JCSS 18, 110–127 (1979)Google Scholar
  4. [T3]
    Tarjan, R.E.: Worst-case analysis of set union algorithms, preprint, Bell LabsGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Norbert Blum
    • 1
  1. 1.Fachbereich 10Universität des SaarlandesSaarbrückenWest-Germany

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