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By Steiner Wolfgang (a-tuwn-dmg, Reviewed Hosam and M. Mahmoud

Abstract

The distribution of m-ary search trees generated by van der Corput sequences. (English summary) Discrete Math. Theor. Comput. Sci. 6 (2004), no. 2, 409–423 (electronic). It has recently become popular to study the structure of a class of labeled trees when constructed from a given mathematical sequence. The present paper adds another sequence to the list of sequences studied in the context of trees. The author considers the van der Corput sequence as input to the m-ary search tree algorithm. As such, the sequence is deterministic and so is the resulting tree. After inserting the first N keys from the van der Corput sequence, the deterministic height is shown to be of logarithmic order in N. When a key is chosen at random from among the first N keys in the sequence, certain aspects become random in the deterministic tree, such as the depth of such a key (its distance from the root). It is shown that the depth of such a random key (under appropriate centering and scaling) is Gaussian, and bounds on the rate of convergence to normality are given. The mean and variance are shown to be logarithmic in N, the proportionality factors are explicitly given (by complicated formulas). The logarithm is to the base q, a defining parameter in the van der Corput sequence. Throughout, the cases when m is an integral power of q are more straightforward and are handled separately

Topics: Algorithms. cf
Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.352.2687
Provided by: CiteSeerX
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