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List Factoring and Relative Worst Order Analysis

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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.

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Notes

  1. In the many papers that discuss \(\operatorname{Randomized-Move-To-Front}\), we have not been able to find a reference to the paper with the first definition of the algorithm. However, [7] cites personal communication with J. Westbrook from 1996 regarding properties of the algorithm.

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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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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark

    Martin R. Ehmsen & Kim S. Larsen

  2. Department of Mathematics and Computer Science and CP³-Origins, University of Southern Denmark, Odense, Denmark

    Jens S. Kohrt

Authors
  1. Martin R. Ehmsen
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  2. Jens S. Kohrt
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  3. Kim S. Larsen
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Correspondence to Kim S. Larsen.

Additional information

A preliminary version of this paper appeared in the proceedings of the 8th Workshop on Approximation and Online Algorithms. This work was supported in part by the Danish Natural Science Research Council.

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Ehmsen, M.R., Kohrt, J.S. & Larsen, K.S. List Factoring and Relative Worst Order Analysis. Algorithmica 66, 287–309 (2013). https://doi.org/10.1007/s00453-012-9637-3

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