On List Update and Work Function Algorithms

  • Eric J. Anderson
  • Kris Hildrum
  • Anna R. Karlin
  • April Rasala
  • Michael Saks
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1643)


The list update problem, a well-studied problem in dynamic data structures, can be described abstractly as a metrical task system. In this paper, we prove that a generic metrical task system algorithm, called the work function algorithm, has constant competitive ratio for list update. In the process, we present a new formulation of the well-known “list factoring” technique in terms of a partial order on the elements of the list. This approach leads to a new simple proof that a large class of online algorithms, including Move-To-Front, is (2 - 1/k)-competitive.


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  1. 1.
    S. Albers and J. Westbrook. Self-organizing data structures. In Online Algorithms: The State of the Art, Fiat-Woeginger, Springer, 1998.Google Scholar
  2. 2.
    D. D. Sleator and R. E. Tarjan. Amortized efficiency of list update and paging rules. Communications of the ACM, 28:202–208, 1985.CrossRefMathSciNetGoogle Scholar
  3. 3.
    J. L. Bentley and C. McGeoch. Amortized analysis of self-organizing sequential search heuristics. Communications of the ACM, 28(4):404–411, 1985.CrossRefGoogle Scholar
  4. 4.
    S. Albers. Improved randomized on-line algorithms for the list update problem. SIAM Journal on Computing, 27: 682–693, 1998.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    R. El-Yaniv. There are infinitely many competitive-optimal online list accessing algorithms. Discussion paper from The Center for Rationality and Interactive Decision Making. Hebrew University.Google Scholar
  6. 6.
    N. Reingold and J. Westbrook. Off-line algorithms for the list update problem. Information Processing Letters, 60(2):75–80, 1996.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    S. Irani. Two results on the list update problem. Information Processing Letters, 38(6):301–306, 1991.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    A. Borodin, N. Linial, and M. Saks. An optimal online algorithm for metrical task systems. Journal of the ACM, 52:46–52, 1985.Google Scholar
  9. 9.
    E. Koutsoupias and C. Papadimitriou. On the k-server conjecture. Journal of the ACM, 42(5): 971–983, September 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    M. Manasse, L. McGeoch and D. D. Sleator. Competitive algorithms for server problems. Journal of Algorithms, 11:208–230, 1990.zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    W. Burley and S. Irani. On algorithm design for metrical task systems. In Proceedings of ACM-SIAM Symposium on Discrete Algorithms, 1995.Google Scholar
  12. 12.
    D. D. Sleator and R. E. Tarjan. Self-adjusting binary search trees. Journal of the ACM, 32: 652–686, 1985.zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    M. Chrobak, L. Larmore. The server problem and on-line games. In On-Line Algorithms, Proceedings of a DIMACS Workshop,Vol 7 of DIMACS Series in Discrete Mathematics and Computer Science, pp. 11–64, 1991.MathSciNetGoogle Scholar
  14. 14.
    W. R. Burley. Traversing layered graphs using the work function algorithm. Journal of Algorithms, 20(3):479–511, 1996.zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    B. Teia. Alower bound for randomized list update algorithms. Information Processing Letters, 47:5–9, 1993.zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    S. Albers, B. von Stengel and R. Werchner. A combined BIT and TIMESTAMP algorithm for the list update problem. Information Processing Letters; 56: 135–139, 1995.zbMATHCrossRefGoogle Scholar
  17. 17.
    S. Albers. Private communication.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Eric J. Anderson
    • 1
  • Kris Hildrum
    • 2
  • Anna R. Karlin
    • 1
  • April Rasala
    • 3
  • Michael Saks
    • 4
  1. 1.Dept. of Computer ScienceUniv. of Wash.
  2. 2.Computer Science Div.Univ. of Calif.
  3. 3.Dept. of Computer ScienceDartmouth CollegeDartmouth
  4. 4.Dept. of MathematicsRutgers Univ.Rutgers

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