Optimal strategies for the list update problem under the MRM alternative cost model

  • Authors:
  • Alexander Golynski;Alejandro López-Ortiz

  • Affiliations:
  • Google Inc., New York City, United States;University of Waterloo, Waterloo, Ontario, Canada

  • Venue:
  • Information Processing Letters
  • Year:
  • 2012

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Abstract

We give an explicit representation for the offline optimum strategy for list update under the MRM model of Martinez and Roura [C. Martinez, S. Roura, On the competitiveness of the move-to-front rule, Theoret. Comput. Sci. 242 (1-2) (2000) 3130-325] and Munro [J.I. Munro, On the competitiveness of linear search, in: Proc. 8th Annual European Symposium on Algorithms (ESA 2000), in: Lecture Notes in Comput. Sci., vol. 1879, 2000, pp. 338-345] and give an O(n^3) algorithm to compute it. This is in contrast to the standard model of Sleator and Tarjan [D.D. Sleator, R.E. Tarjan, Amortized efficiency of list update and paging rules, Commun. ACM 28 (2) (1985) 202-208] under which computing the offline optimum was shown to be NP-hard [C. Ambuhl, Offline list update is NP-hard, in: Proc. 8th Annual European Symposium on Algorithms (ESA 2000), in: Lecture Notes in Comput. Sci., vol. 1879, 2000, pp. 42-51]. This algorithm follows from a new characterization theorem for realizable visiting sequences in the MRM model.