List Factoring and Relative Worst Order Analysis

  • Martin R. Ehmsen
  • Jens S. Kohrt
  • Kim S. Larsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6534)


Relative worst order analysis is a supplement or alternative to competitive analysis which has been shown to give results more in accordance with observed behavior of online algorithms for a range of different online problems. The contribution of this paper is twofold. First, it adds the static list accessing problem to the collection of online problems where relative worst order analysis gives better results. Second, and maybe more interesting, it adds the non-trivial supplementary proof technique of list factoring to the theoretical toolbox for relative worst order analysis.


Competitive Ratio Online Algorithm Deterministic Algorithm Static List Initial List 
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.
    Albers, S.: Improved randomized on-line algorithms for the list update problem. SIAM Journal on Computing 27(3), 682–693 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Albers, S., Lauer, S.: On list update with locality of reference. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 96–107. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  3. 3.
    Albers, S., von Stengel, B., Werchner, R.: A combined BIT and TIMESTAMP algorithm for the list update problem. Information Processing Letters 56, 135–139 (1995)CrossRefzbMATHGoogle Scholar
  4. 4.
    Albers, S., Westbrook, J.: Self-organizing data structures. In: Fiat, A., Woeginger, G.J. (eds.) Online Algorithms — The State of the Art. LNCS, vol. 1442, pp. 13–51. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  5. 5.
    Angelopoulos, S., Dorrigiv, R., López-Ortiz, A.: On the separation and equivalence of paging strategies. In: 18th ACM-SIAM Symposium on Discrete Algorithms, pp. 229–237 (2007)Google Scholar
  6. 6.
    Angelopoulos, S., Dorrigiv, R., López-Ortiz, A.: List update with locality of reference. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds.) LATIN 2008. LNCS, vol. 4957, pp. 399–410. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Bachrach, R., El-Yaniv, R.: Online list accessing algorithms and their applications: Recent empirical evidence. In: Proceedings of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 53–62 (1997)Google Scholar
  8. 8.
    Ben-David, S., Borodin, A.: A New Measure for the Study of On-Line Algorithms. Algorithmica 11, 73–91 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Bentley, J.L., McGeoch, C.C.: Amortized analyses of self-organizing sequential search heuristics. Communications of the ACM 28, 404–411 (1985)CrossRefGoogle Scholar
  10. 10.
    Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)zbMATHGoogle Scholar
  11. 11.
    Boyar, J., Favrholdt, L.M.: The relative worst order ratio for on-line algorithms. ACM Transactions on Algorithms 3(2), article 22 (2007)Google Scholar
  12. 12.
    Boyar, J., Favrholdt, L.M., Larsen, K.S.: The relative worst-order ratio applied to paging. Journal of Computer and System Sciences 73, 818–843 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Boyar, J., Irani, S., Larsen, K.S.: A Comparison of Performance Measures for Online Algorithms. In: Dehne, F., Gavrilova, M., Sack, J.-R., Tóth, C.D. (eds.) WADS 2009. LNCS, vol. 5664, pp. 119–130. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  14. 14.
    Boyar, J., Medvedev, P.: The relative worst order ratio applied to seat reservation. ACM Transactions on Algorithms 4(4), article 48 (2008)Google Scholar
  15. 15.
    Dorrigiv, R., Ehmsen, M.R., López-Ortiz, A.: Parameterized analysis of paging and list update algorithms. In: Bampis, E., Jansen, K. (eds.) WAOA 2009. LNCS, vol. 5893, pp. 104–115. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  16. 16.
    Dorrigiv, R., López-Ortiz, A.: A Survey of Performance Measures for On-line Algorithms. SIGACT News 36(3), 67–81 (2005)CrossRefGoogle Scholar
  17. 17.
    Ehmsen, M.R., Kohrt, J.S., Larsen, K.S.: List factoring and relative worst order analysis (2010); arXiv:1009.5787Google Scholar
  18. 18.
    Epstein, L., Favrholdt, L.M., Kohrt, J.S.: Comparing online algorithms for bin packing problems. Journal of Scheduling (accepted for publication)Google Scholar
  19. 19.
    Epstein, L., Favrholdt, L.M., Kohrt, J.S.: Separating scheduling algorithms with the relative worst order ratio. Journal of Combinatorial Optimization 12(4), 362–385 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Garefalakis, T.: A new family of randomized algorithms for list accessing. In: Burkard, R.E., Woeginger, G.J. (eds.) ESA 1997. LNCS, vol. 1284, pp. 200–216. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  21. 21.
    Graham, R.L.: Bounds on multiprocessing timing anomalies. SIAM Journal on Applied Mathematics 17(2), 416–429 (1969)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Irani, S.: Two results on the list update problem. Information Processing Letters 38(6), 301–306 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Karlin, A.R., Manasse, M.S., Rudolph, L., Sleator, D.D.: Competitive snoopy caching. Algorithmica 3, 79–119 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Kenyon, C.: Best-fit bin-packing with random order. In: 7th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 359–364 (1996)Google Scholar
  25. 25.
    Koutsoupias, E., Papadimitriou, C.H.: Beyond Competitive Analysis. SIAM Journal on Computing 30(1), 300–317 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Krumke, S.O., de Paepe, W.E., Rambau, J., Stougie, L.: Bincoloring. Theoretical Computer Science 407(1-3), 231–241 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    McCabe, J.: On serial files with relocatable records. Operations Research 13(4), 609–618 (1965)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Reingold, N., Westbrook, J., Sleator, D.D.: Randomized competitive algorithms for the list update problem. Algorithmica 11, 15–32 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Communications of the ACM 28(2), 202–208 (1985)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Teia, B.: A lower bound for randomized list update algorithms. Information Processing Letters 47, 5–9 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Young, N.: The k-server dual and loose competitiveness for paging. Algorithmica 11, 525–541 (1994)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Martin R. Ehmsen
    • 1
  • Jens S. Kohrt
    • 1
    • 2
  • Kim S. Larsen
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkOdenseDenmark
  2. 2.CP3-OriginsUniversity of Southern DenmarkOdenseDenmark

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