A constant update time finger search tree

  • Paul Dietz
  • Rajeev Raman
Theory Of Computing, Algorithms And Programming
Part of the Lecture Notes in Computer Science book series (LNCS, volume 468)


Levcopolous and Overmars [12] describe a search tree in which the time to insert or delete a key is O(1) once the position of the key to be inserted or deleted was known. Their data structure does not support fingers, pointers to points of high access or update activity in the set such that access and update operations in the vicinity of a finger are particularly efficient [3, 8, 10, 11, 15]. Levcopolous and Overmars leave as an open question whether a data structure can be designed which allowed updates in constant time and supports fingers. We answer the question in the affirmative by giving an algorithm in the RAM with logarithmic word size model [1].

CR Classification Number

[F.2.2 - Sorting and Searching] 


Real-Time Algorithm Search Tree Fingers 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. V. Aho, J. E. Hopcroft, and J. D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, 1974.Google Scholar
  2. [2]
    C. Aragon and R. Seidel. Randomized search trees. In Proc. 30th IEEE FOCS, pages 540–545, 1989.Google Scholar
  3. [3]
    M. Brown and R. Tarjan. Design and analysis of a data structure for representing sorted lists. SIAM Journal of Computing, 1980.Google Scholar
  4. [4]
    P. Dietz and R. Raman. A constant update time finger search tree. Technical Report 321, University of Rochester Computer Science Department, 1989.Google Scholar
  5. [5]
    P. Dietz and D. Sleator. Two algorithms for maintaining order in a list. In Proc. 19th ACM STOC, pages 365–372, 1987.Google Scholar
  6. [6]
    J. Driscoll, N. Sarnak, D. Sleator, and R. Tarjan. Making data structures persistent. Journal of Computer and System Science, 38:86–124, 1989.Google Scholar
  7. [7]
    H. N. Gabow and R. E. Tarjan. A linear-time algorithm for a special case of disjoint set union. Journal of Computer and System Science, 30:209–221, 1985.Google Scholar
  8. [8]
    L. Guibas, E. McCreight, M. Plass, and J. Roberts. A new representation for sorted lists. In Proc. 9th ACM STOC, pages 49–60, 1977.Google Scholar
  9. [9]
    D. Harel. Fast updates with a guaranteed time bound per update. Technical Report 154, University of California, Irvine, 1980.Google Scholar
  10. [10]
    S. Huddleston and K. Mehlhorn. A new data structure for representing sorted lists. Acta Informatica, 17:157–184, 1982.Google Scholar
  11. [11]
    S. R. Kosaraju. Localized search in sorted lists. In Proc. 13th ACM STOC, pages 62–69, 1981.Google Scholar
  12. [12]
    C. Levcopolous and M. H. Overmars. A balanced search tree with O(1) worst-case update time. Acta Informatica, 26:269–278, 1988.Google Scholar
  13. [13]
    M. Overmars. A O(1) average time update scheme for balanced binary search trees. Bull. EATCS, pages 27–29, 1982.Google Scholar
  14. [14]
    M. H. Overmars. The design of dynamic data structures, LNCS 156. Springer-Verlag, 1983.Google Scholar
  15. [15]
    A. K. Tsakalidis. AVL-trees for localized search. Information and Control, 67:173–194, 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Paul Dietz
    • 1
  • Rajeev Raman
    • 1
  1. 1.Department of Computer ScienceUniversity of RochesterRochester

Personalised recommendations