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Optimal Worst-Case Operations for Implicit Cache-Oblivious Search Trees

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Algorithms and Data Structures (WADS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2748))

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Abstract

We close an open issue on dictionaries dating back to the sixthies. An array of n keys can be sorted so that searching takes O(log n) time. Alternatively, it can be organized as a heap so that inserting and deleting keys take O(log n) time. We show that these bounds can be simultaneously achieved in the worst case for searching and updating by suitably maintaining a permutation of the n keys in the array. The resulting data structure is called implicit as it uses just O(1) extra memory cells beside the n cells for the array. The data structure is also cache-oblivious, attaining O(logB n) block transfers in the worst case for any (unknown) value of the block size B, without wasting any single cell of memory at any level of the memory hierarchy.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, via Buonarroti 2, 56127, Pisa, Italy

    Gianni Franceschini & Roberto Grossi

Authors
  1. Gianni Franceschini
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  2. Roberto Grossi
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Editor information

Editors and Affiliations

  1. Carleton University, Ottawa, Canada

    Frank Dehne

  2. School of Computer Science, Carleton University, 1125 Colonel By Drive, K1S 5B6, Ottawa, Canada

    Jörg-Rüdiger Sack

  3. School of Computer Science, Carleton University, K1S 5B6, Ottawa, ON, Canada

    Michiel Smid

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© 2003 Springer-Verlag Berlin Heidelberg

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Franceschini, G., Grossi, R. (2003). Optimal Worst-Case Operations for Implicit Cache-Oblivious Search Trees. In: Dehne, F., Sack, JR., Smid, M. (eds) Algorithms and Data Structures. WADS 2003. Lecture Notes in Computer Science, vol 2748. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45078-8_11

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  • DOI: https://doi.org/10.1007/978-3-540-45078-8_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40545-0

  • Online ISBN: 978-3-540-45078-8

  • eBook Packages: Springer Book Archive

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