Abstract
We prove that no algorithm for balanced binary search trees performing insertions and deletions in amortized time O(f(n)) can guarantee a height smaller than [log(n + 1) + 1/f(n)] for all n. We improve the existing upper bound to [log(n + 1) + log2 (f(n))/f(n)], thus almost matching our lower bound. We also improve the existing upper bound for worst case algorithms, and give a lower bound for the semi-dynamic case.
Supported by the Danish National Science Research Council (grant no. 11-0575) and by the ESPRIT Long Term Research Programme of the EU under project no. 20244 (ALCOM-IT). Part of this research was done while visiting the Department of Computer Science, University of Waterloo, Canada.
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Fagerberg, R. (1996). Binary search trees: How low can you go?. In: Karlsson, R., Lingas, A. (eds) Algorithm Theory — SWAT'96. SWAT 1996. Lecture Notes in Computer Science, vol 1097. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61422-2_151
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DOI: https://doi.org/10.1007/3-540-61422-2_151
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