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Algorithmica

, Volume 66, Issue 2, pp 287–309 | Cite as

List Factoring and Relative Worst Order Analysis

  • Martin R. Ehmsen
  • Jens S. Kohrt
  • Kim S. Larsen
Article

Abstract

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. As the first contribution, it adds the static list accessing problem to the collection of online problems where relative worst order analysis gives better results. List accessing is a classic data structuring problem of maintaining optimal ordering in a linked list. It is also one of the classic problems in online algorithms, in that it is used as a model problem, along with paging and a few other problems, when trying out new techniques and quality measures. As the second contribution, this paper adds the non-trivial supplementary proof technique of list factoring to the theoretical toolbox for relative worst order analysis. List factoring is perhaps the most successful technique for analyzing list accessing algorithms, reducing the complexity of the analysis of algorithms on full-length lists to lists of length two.

Keywords

Online algorithms List accessing Relative worst order analysis List factoring 

Notes

Acknowledgements

The authors would like to thank Joan Boyar for initial discussions on the relationship between \(\operatorname{MTF}\) and \(\operatorname{TRANS}\) and the anonymous referees for constructive suggestions for improving the paper.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

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

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