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The Power and Limitations of Static Binary Search Trees with Lazy Finger

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Algorithms and Computation (ISAAC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8889))

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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.

Research for P. Bose supported in part by NSERC.

Research partially completed at NYU School of Engineering with support from NSF grant CCF-1319648. Research partially completed at Université Libre de Bruxelles with support from FNRS. Research partially completed at and supported by MADALGO, a center of the Danish National Research Foundation.

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

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Author information

Authors and Affiliations

  1. Carleton University, Ottawa, ON, Canada

    Presenjit Bose

  2. New York University, Shanghai, China

    John Iacono

  3. Université Libre de Bruxelles, Brussels, Belgium

    Karim Douïeb & Stefan Langerman

Authors
  1. Presenjit Bose
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  2. Karim Douïeb
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  3. John Iacono
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  4. Stefan Langerman
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Corresponding author

Correspondence to John Iacono .

Editor information

Editors and Affiliations

  1. Pohang University of Science and Technology, Pohang, Korea, Republic of (South Korea)

    Hee-Kap Ahn

  2. Hankuk University of Foreign Studies, Yongin-si, Korea, Republic of (South Korea)

    Chan-Su Shin

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Bose, P., Douïeb, K., Iacono, J., Langerman, S. (2014). The Power and Limitations of Static Binary Search Trees with Lazy Finger. In: Ahn, HK., Shin, CS. (eds) Algorithms and Computation. ISAAC 2014. Lecture Notes in Computer Science(), vol 8889. Springer, Cham. https://doi.org/10.1007/978-3-319-13075-0_15

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  • DOI: https://doi.org/10.1007/978-3-319-13075-0_15

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  • Print ISBN: 978-3-319-13074-3

  • Online ISBN: 978-3-319-13075-0

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