Poketree: A Dynamically Competitive Data Structure with Good Worst-Case Performance

  • Jussi Kujala
  • Tapio Elomaa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4288)


We introduce a new O(lg lg n)-competitive binary search tree data structure called poketree that has the advantage of attaining, under worst-case analysis, O(lg n) cost per operation, including updates. Previous O(lg lg n)-competitive binary search tree data structures have not achieved O(lg n) worst-case cost per operation. A standard data structure such as red-black tree or deterministic skip list can be augmented with the dynamic links of a poketree to make it O(lg lg n)-competitive. Our approach also uses less memory per node than previous competitive data structures supporting updates.


Competitive Ratio Binary Search Static Successor Static Link Reference Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Bayer, R.: Symmetric binary B-trees: Data structure and maintenance algorithms. Acta Informatica 1, 290–306 (1972)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bayer, R., McCreight, E.M.: Organization and maintenance of large ordered indices. Acta Informatica 1, 173–189 (1972)CrossRefGoogle Scholar
  3. 3.
    Sleator, D.D., Tarjan, R.E.: Self-adjusting binary search trees. Journal of the ACM 32(3), 652–686 (1985)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Pugh, W.: Skip lists: A probabilistic alternative to balanced trees. Communications of the ACM 33(6), 668–676 (1990)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Munro, I., Papadakis, T., Sedgewick, R.: Deterministic skip lists. In: Proceedings of the 3rd Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 367–375. SIAM, Philadelphia (1992)Google Scholar
  6. 6.
    Demaine, E.D., Harmon, D., Iacono, J., Pǎtraşcu, M.: Dynamic optimality – almost. In: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, pp. 484–490. IEEE Computer Society Press, Los Alamitos (2004)CrossRefGoogle Scholar
  7. 7.
    Wilber, R.: Lower bounds for accessing binary search trees with rotations. SIAM Journal on Computing 18(1), 56–67 (1989)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Wang, C.C., Derryberry, J., Sleator, D.D.: O(loglogn)-competitive dynamic binary search trees. In: Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 374–383. ACM Press, New York (2006)CrossRefGoogle Scholar
  9. 9.
    Tarjan, R.E.: Sequential access in splay trees takes linear time. Combinatorica 5(4), 367–378 (1985)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Culik II, K., Wood, D.: A note on some tree similarity measures. Information Processing Letters 15(1), 39–42 (1982)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. McGraw-Hill, New York (2001)MATHGoogle Scholar
  12. 12.
    Tarjan, R.E.: Data Structures and Network Algorithms. SIAM, Philadelphia (1983)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jussi Kujala
    • 1
  • Tapio Elomaa
    • 1
  1. 1.Institute of Software SystemsTampere University of TechnologyTampereFinland

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