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)


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.


Search Tree Search Path Binary Search Tree Jump Pointer Search Operation 
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  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

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