The power and limitations of static binary search trees with lazy finger

Presenjit Bose, Karim Douïeb, John Iacono, Stefan Langerman

    Research output: Chapter in Book/Report/Conference proceedingChapter

    Abstract

    A static binary search tree where every search starts from where the previous one ends (lazy finger) is considered. Such a search method is more powerful than that of the classic optimal static trees, where every search starts from the root (root finger), and less powerful than when rotations are allowed—where finding the best rotation based tree is the topic of the dynamic optimality conjecture of Sleator and Tarjan. The runtime of the classic root-finger tree can be expressed in terms of the entropy of the distribution of the searches, but we show that this is not the case for the optimal lazy finger tree. A non-entropy based asymptotically-tight expression for the runtime of the optimal lazy finger trees is derived, and a dynamic programming-based method is presented to compute the optimal tree.

    Original languageEnglish (US)
    Title of host publicationAlgorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings
    EditorsHee-Kap Ahn, Chan-Su Shin
    PublisherSpringer Verlag
    Pages181-192
    Number of pages12
    ISBN (Electronic)9783319130743
    DOIs
    StatePublished - 2014

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume8889
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

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  • Cite this

    Bose, P., Douïeb, K., Iacono, J., & Langerman, S. (2014). The power and limitations of static binary search trees with lazy finger. In H-K. Ahn, & C-S. Shin (Eds.), Algorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings (pp. 181-192). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8889). Springer Verlag. https://doi.org/10.1007/978-3-319-13075-0_15