Abstract
This paper presents an analytic approach to the construction cost of fringe-balanced binary search trees. In [7], Mahmoud used a bottom-up approach and an urn model of Pólya. The present method is top-down and uses differential equations and Hwang's quasi-power theorem to derive the asymptotic normality of the number of rotations needed to construct such afringe balanced search tree. We also obtain the exact expectation and variance with this method. Although Pólya's urn model is no longer needed, we also present an elegant analysis of it based on an operator calculus as in [4].
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This research was supported by the Austrian Research Society (FWF) under the project number P12599-MAT.
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Panholzer, A., Prodinger, H. An analytic approach for the analysis of rotations in fringe-balanced binary search trees. Annals of Combinatorics 2, 173–184 (1998). https://doi.org/10.1007/BF01608487
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DOI: https://doi.org/10.1007/BF01608487