How to Splay for loglogN-Competitiveness

  • George F. Georgakopoulos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3503)


We present an extension of the splay technique, the chain-splay. Chain-splay trees splay the accessed element to the root exactly as classic splay trees do, but also perform some local ‘house-keeping’ splay operations below the accessed element. We prove that chain-splay is loglogN-competitive to any off-line searching algorithm. This result is the nearest point to dynamic optimality of splay trees reached since 1983.


Transition Point Dynamic Optimality Head Node Balance Tree Binary Search 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Adel’son-Vel’ski, G.M., Landis, E.M.: An Algorithm for the Organization of Information. Soviet Mathematical Doklady 146, 1259–1263 (1962)Google Scholar
  2. 2.
    Albers, S., Westbrook, J.: Self-Organizing Data-Structures. In: Fiat, A. (ed.) Dagstuhl Seminar 1996, vol. 1442. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  3. 3.
    Allen, B., Munro, I.J.: Self Organizing Binary Search Trees. J. of the ACM 25(4), 526–535 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Balasubramanian, R., Raman, V.: Path Balance Heuristic For Self-Adjusting Binary Search Trees. In: Thiagarajan, P.S. (ed.) FSTTCS 1995, vol. 1026, pp. 338–348. Springer, Heidelberg (1995)Google Scholar
  5. 5.
    Bayer, R., McCreight, E.: Organization and Maintenance of Large Ordered Indexes. Acta Informatica 1(3), 173–189 (1972)CrossRefGoogle Scholar
  6. 6.
    Blum, A., Chawla, S., Kalai, A.: Static Optimality and Dynamic Search-Optimality in Lists and Trees. In: ACM-SIAM Symp. on Discrete Algorithms, 13th, San Francisco, USA, January 6–8, pp. 1–8 (2002)Google Scholar
  7. 7.
    Cole, R.J.: On the Dynamic Finger Conjecture for Splay Trees, Part II: The Proof. SIAM J. on Computing 30(1), 44–85 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Cole, R.J., Mishra, B., Schmidt, J.P., Siegel, A.: On the Dynamic Finger Conjecture for Splay Trees, Part I: Splaying Sorting in log n-Block Sequences. SIAM J. on Computing 30(1), 1–43 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Demaine, D.E., Harmon, D., Iacono, J., Pătraşcu, M.: Dynamic Optimality—Almost. In: IEEE Symp. on the Foundations of Computer Science, 45th, Rome, Italy, October 17–19, pp. 484–490 (2004)Google Scholar
  10. 10.
    Fürer, M.: Randomized Splay Trees. In: ACM-SIAM Symp. on Discrete Algorithms, 10th, Maryland, USA, January 17–19, pp. 903–904 (1999)Google Scholar
  11. 11.
    Georgakopoulos, G.F.: Splay Trees: a Reweighing Lemma and a Proof of Competitiveness vs. Dynamic Balanced Trees. J. of Algorithms 51, 64–76 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Georgakopoulos, G.F., McClurkin, D.J.: Sphendamnoe: A Proof that k-Splay Falls to Achieve logk N Behaviour. In: Manolopoulos, Y., Evripidou, S., Kakas, A.C. (eds.) PCI 2001, vol. 2563, pp. 480–496. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    Georgakopoulos, G.F., McClurkin, D.J.: General Template Splay: A Basic Theory and Calculus. The Computer Journal 41(1), 10–19 (2004)CrossRefGoogle Scholar
  14. 14.
    Iacono, J.: Key Iindependent Optimality. In: Bose, P., Morin, P. (eds.) ISAAC 2002, vol. 2518, pp. 25–31. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  15. 15.
    Knuth, D.E.: Optimum Binary Search Trees. Acta Informatica 1, 14–25 (1971)zbMATHCrossRefGoogle Scholar
  16. 16.
    Martel, C.: Self-Adjusting Multi-Way Search Trees. Information Processing Letters 38(3), 135–141 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Overmars, M.H.: The Design of Dynamic Data Structures, vol. 156. Springer, Heidelberg (1983)zbMATHGoogle Scholar
  18. 18.
    Sherk, M.: Self Adjusting k-ary Search Trees. J. of Algorithms 19, 25–44 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Sleator, D.D., Tarjan, R.E.: Self Adjusting Binary Search Trees. J. of the ACM 32(3), 652–686 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Subramanian, A.: An Explanation of Splaying. J. of Algorithms 20, 512–525 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Sundar, R.: Twists, Turns, Cascades, Dequeue Conjecture and Scanning Theorem. In: IEEE Symp. on the Foundations of Computer Science, 30th, North Carolina, USA, October 30 – November 1, pp. 555–559 (1989)Google Scholar
  22. 22.
    Tarjan, R.E.: Amortized Computational Complexity. J. of Applied and Discrete Mathematics 6(2), 306–318 (1985)zbMATHMathSciNetGoogle Scholar
  23. 23.
    Wilber, R.: Lower Bounds for Accessing Binary Search Trees with Rotations. SIAM J. on Computing 18(1), 56–67 (1989)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • George F. Georgakopoulos
    • 1
  1. 1.Dept. of Computer ScienceUniversity of CreteHeraklionGreece

Personalised recommendations