Advertisement

Skip Lift: A Probabilistic Alternative to Red-Black Trees

  • Prosenjit Bose
  • Karim Douïeb
  • Pat Morin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6460)

Abstract

We present the Skip lift, a randomized dictionary data structure inspired by the skip list [Pugh ’90, Comm. of the ACM]. Similar to the skip list, the skip lift has the finger search property: Given a pointer to an arbitrary element f, searching for an element x takes expected O(logδ) time where δ is the rank distance between the elements x and f. The skip lift uses nodes of O(1) worst-case size and it is one of the few efficient dictionary data structures that performs an O(1) worst-case number of structural changes during an update operation. Given a pointer to the element to be removed from the skip lift the deletion operation takes O(1) worst-case time.

Keywords

Search Tree Search Path Binary Search Tree Jump Pointer Search Operation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aragon, C.R., Seidel, R.: Randomized search trees. Algorithmica 16, 464–497 (1996)CrossRefzbMATHGoogle Scholar
  2. 2.
    Bagchi, A., Buchsbaum, A.L., Goodrich, M.T.: Biased skip lists. Algorithmica 42(1), 31–48 (2005)CrossRefzbMATHGoogle Scholar
  3. 3.
    Bayer, R., McCreight, E.: Organization and maintenance of large ordered indexes. Acta Informatica 1, 173–189 (1972)CrossRefzbMATHGoogle Scholar
  4. 4.
    Bent, S.W., Sleator, D., Tarjan, R.: Biased search trees. SIAM Journal on Computing 14(3), 545–568 (1985)CrossRefzbMATHGoogle Scholar
  5. 5.
    Bose, P., Douïeb, K., Langerman, S.: Dynamic optimality for skip lists and B-trees. In: Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2008), pp. 1106–1114 (2008)Google Scholar
  6. 6.
    Brodal, G.S., Lagogiannis, G., Makris, C., Tsakalidis, A.K., Tsichlas, K.: Optimal finger search trees in the pointer machine. J. Comput. Syst. Sci. 67(2), 381–418 (2003)CrossRefzbMATHGoogle Scholar
  7. 7.
    Brönnimann, H., Cazals, F., Durand, M.: Randomized jumplists: A jump-and-walk dictionary data structure. In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 283–294. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Cho, S., Sahni, S.: Weight-biased leftist trees and modified skip lists. J. Exp. Algorithmics 3, 2 (1998)CrossRefzbMATHGoogle Scholar
  9. 9.
    Feigenbaum, J., Tarjan, R.: Two new kinds of biased search trees. Bell System Technical Journal 62(10), 3139–3158 (1983)CrossRefzbMATHGoogle Scholar
  10. 10.
    Fleischer, R.: A simple balanced search tree with O(1) worst-case update time. International Journal of Foundations of Computer Science 7, 137–149 (1996)CrossRefzbMATHGoogle Scholar
  11. 11.
    Haeupler, B., Sen, S., Tarjan, R.E.: Rank-balanced trees. In: Dehne, F., Gavrilova, M., Sack, J.-R., Tóth, C.D. (eds.) WADS 2009. LNCS, vol. 5664, pp. 351–362. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  12. 12.
    Leonidas, R.S., Guibas, J.: A dichromatic framework for balanced trees. In: Proc. 19th IEEE Symp. on Foundations of Computer Science, pp. 8–21 (1978)Google Scholar
  13. 13.
    Levcopoulos, C., Overmars, M.: A balanced search tree with O(1) worst-case update time. Acta Informatica 26(3), 269–277 (1988)CrossRefzbMATHGoogle Scholar
  14. 14.
    Martinez, C., Roura, S.: Optimal and nearly optimal static weighted skip lists. Technical report, LSI-95-34-R, Dept. Llenguatges i Sistemes Informàtics (Universitat Politèchnica de Catalunya) (1995)Google Scholar
  15. 15.
    Martínez, C., Roura, S.: Randomized binary search trees. J. ACM 45(2), 288–323 (1998)CrossRefzbMATHGoogle Scholar
  16. 16.
    Munro, I., Papadakis, T., Sedgewick, R.: Deterministic skip lists. In: Proceedings of the Third Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 367–375 (1992)Google Scholar
  17. 17.
    Papadakis, T.: Skip lists and probabilistic analysis of algorithms. PhD thesis, University of Waterloo, Department of Computer Science and Faculty of Mathematics (Available as Tech. Report CS-93-28) (1993)Google Scholar
  18. 18.
    Pugh, W.: Skip lists: a probabilistic alternative to balanced trees. Communications of the ACM 33(6), 668–676 (1990)CrossRefGoogle Scholar
  19. 19.
    Tarjan, R.E.: Updating a Balanced Search Tree in O(1) Rotations. Inf. Process. Lett. 16(5), 253–257 (1983)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Prosenjit Bose
    • 1
  • Karim Douïeb
    • 1
  • Pat Morin
    • 1
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada

Personalised recommendations