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Rank aggregation in cyclic sequences

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Abstract

In this paper we propose the problem of finding the cyclic sequence which best represents a set of cyclic sequences. Given a set of elements and a precedence cost matrix we look for the cyclic sequence of the elements which is at minimum distance from all the ranks when the permutation metric distance is the Kendall Tau distance. In other words, the problem consists of finding a robust cyclic rank with respect to a set of elements. This problem originates from the Rank Aggregation Problem for combining different linear ranks of elements. Next, we also introduce the problem of finding the cyclic sequence with minimum expected cost with respect to a probability measure based on dissimilarity between cyclic sequences on the Kendall Tau metric. Finally, we establish certain relationships among some classical problems and the new problems that we have proposed.

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Acknowledgments

This work was partly supported by the Spanish Ministry of Economy and Competitiveness through Grants MTM2013-46962-C02-01, MTM2015-68097-P (MINECO/FEDER) and by Regional Government of Andalucía Grant FQM5849.

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Authors and Affiliations

  1. Department of Statistics, Mathematics and Computer Science, Center of Operations Research, Miguel Hernández University of Elche, Elche, Spain

    Eva M. García-Nové, Javier Alcaraz, Mercedes Landete & Juan F. Monge

  2. IMUS, University of Seville, Seville, Spain

    Justo Puerto

Authors
  1. Eva M. García-Nové
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  2. Javier Alcaraz
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  3. Mercedes Landete
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  4. Juan F. Monge
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  5. Justo Puerto
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Correspondence to Mercedes Landete.

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García-Nové, E.M., Alcaraz, J., Landete, M. et al. Rank aggregation in cyclic sequences. Optim Lett 11, 667–678 (2017). https://doi.org/10.1007/s11590-016-1047-z

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  • DOI: https://doi.org/10.1007/s11590-016-1047-z

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