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
Mehlhorn, K.: Data structures and algorithms 1, Sorting and Searching, Springer-Verlag (1984)
Tarjan, R.E.: Efficiency of a good but not linear set union algorithm, JACM 22, 215–225 (1975)
Tarjan, R.E.: A class of algorithms which require nonlinear time to maintain disjoint sets, JCSS 18, 110–127 (1979)
Tarjan, R.E.: Worst-case analysis of set union algorithms, preprint, Bell Labs
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© 1984 Springer-Verlag Berlin Heidelberg
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Blum, N. (1984). On the single-operation worst-case time complexity of the disjoint set union problem. In: Mehlhorn, K. (eds) STACS 85. STACS 1985. Lecture Notes in Computer Science, vol 182. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023992
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DOI: https://doi.org/10.1007/BFb0023992
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