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Belga B-Trees

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Computer Science – Theory and Applications (CSR 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11532))

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Abstract

We revisit self-adjusting external memory tree data structures, which combine the optimal (and practical) worst-case I/O performances of B-trees, while adapting to the online distribution of queries. Our approach is analogous to undergoing efforts in the BST model, where Tango Trees (Demaine et al. 2007) were shown to be \(O(\log \log N)\)-competitive with the runtime of the best offline binary search tree on every sequence of searches. Here we formalize the B-Tree model as a natural generalization of the BST model. We prove lower bounds for the B-Tree model, and introduce a B-Tree model data structure, the Belga B-tree, that executes any sequence of searches within a \(O(\log \log N)\) factor of the best offline B-tree model algorithm, provided \(B=\log ^{O(1)}N\). We also show how to transform any static BST into a static B-tree which is faster by a \(\varTheta (\log B)\) factor; the transformation is randomized and we show that randomization is necessary to obtain any significant speedup.

The full version of this paper can be found at: https://arxiv.org/pdf/1903.03560.pdf.

J. Iacono—Research supported by the Fonds de la Recherche Scientifique-FNRS under Grant no MISU F 6001 1.

J. Iacono—Research supported by NSF Grant CCF-1533564.

S. Langerman—Directeur de Recherches du F.R.S-FNRS.

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Notes

  1. 1.

    The Tango tree was invented on an overnight flight from JFK airport en route to Buenos Aires, Argentina. The work on the Belga B-Tree has been substantially completed at Cafe Belga, Ixelles, Belgium.

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Authors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, USA

    Erik D. Demaine

  2. Université Libre de Bruxelles, Brussels, Belgium

    John Iacono, Grigorios Koumoutsos & Stefan Langerman

  3. New York University, New York, USA

    John Iacono

Authors
  1. Erik D. Demaine
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  2. John Iacono
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  3. Grigorios Koumoutsos
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  4. Stefan Langerman
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Corresponding author

Correspondence to Grigorios Koumoutsos .

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Editors and Affiliations

  1. Novosibirsk State University, Novosibirsk, Russia

    René van Bevern

  2. Laboratoire d'Informatique Gaspard-Monge, Marne-la-Vallée, France

    Gregory Kucherov

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Demaine, E.D., Iacono, J., Koumoutsos, G., Langerman, S. (2019). Belga B-Trees. In: van Bevern, R., Kucherov, G. (eds) Computer Science – Theory and Applications. CSR 2019. Lecture Notes in Computer Science(), vol 11532. Springer, Cham. https://doi.org/10.1007/978-3-030-19955-5_9

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  • DOI: https://doi.org/10.1007/978-3-030-19955-5_9

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