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On some properties of (a,b)-trees

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Optimal Algorithms (OA 1989)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 401))

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Abstract

In this paper some properties of (a,b)-trees are studied. Such trees are a generalization of B-trees and therefore their performances are dependent upon their height. Hence it is important to be able to enumerate the (a,b)-trees of a given height. To this purpose, a recurrence relation is defined which cannot be solved by the usual techniques. Therefore some limitations are established to the number of (a,b)-trees of a given height and an approximate formula is given which shows that the sequence of such numbers is a doubly exponential one. As a consequence of this fact, some properties, as for instance the probability that the height grows by the effects of an insertion, are studied using “profiles”. The proofs are given of how profiles are generated and how from a profile one can get the number of corresponding (a,b)-trees.

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References

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Authors and Affiliations

  1. Dipartimento di Matematica Pura e Applicata, Universitá di Padova, Italy

    Renzo Sprugnoli

  2. Dipartimento di Sistemi e Informatica, Universitá di Firenze, Italy

    Elena Barcucci, Alessandra Chiuderi & Renzo Pinzani

Authors
  1. Renzo Sprugnoli
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  2. Elena Barcucci
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  3. Alessandra Chiuderi
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  4. Renzo Pinzani
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Editor information

Hristo Djidjev

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© 1989 Springer-Verlag Berlin Heidelberg

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Sprugnoli, R., Barcucci, E., Chiuderi, A., Pinzani, R. (1989). On some properties of (a,b)-trees. In: Djidjev, H. (eds) Optimal Algorithms. OA 1989. Lecture Notes in Computer Science, vol 401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51859-2_13

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  • DOI: https://doi.org/10.1007/3-540-51859-2_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51859-4

  • Online ISBN: 978-3-540-46831-8

  • eBook Packages: Springer Book Archive

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