Algorithmica

, Volume 76, Issue 4, pp 1264–1275

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

  • Prosenjit Bose
  • Karim Douïeb
  • John Iacono
  • Stefan Langerman
Article

DOI: 10.1007/s00453-016-0224-x

Cite this article as:
Bose, P., Douïeb, K., Iacono, J. et al. Algorithmica (2016) 76: 1264. doi:10.1007/s00453-016-0224-x
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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.

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Prosenjit Bose
    • 1
  • Karim Douïeb
    • 4
  • John Iacono
    • 2
  • Stefan Langerman
    • 3
  1. 1.Carleton UniversityOttawaCanada
  2. 2.New York UniversityBrooklynUSA
  3. 3.Université Libre de BruxellesBrusselsBelgium
  4. 4.ForestBelgium

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