Fixed-Parameter Algorithms for Kemeny Scores

Authors:
Nadja Betzler;Michael R. Fellows;Jiong Guo;Rolf Niedermeier;Frances A. Rosamond
Affiliations:
Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany D-07743;PC Research Unit, Office of DVC (Research), University of Newcastle, Callaghan, Australia NSW 2308;Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany D-07743;Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany D-07743;PC Research Unit, Office of DVC (Research), University of Newcastle, Callaghan, Australia NSW 2308
Venue:
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
Year:
2008

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Abstract

The Kemeny Scoreproblem is central to many applications in the context of rank aggregation. Given a set of permutations (votes) over a set of candidates, one searches for a "consensus permutation" that is "closest" to the given set of permutations. Computing an optimal consensus permutation is NP-hard. We provide first, encouraging fixed-parameter tractability results for computing optimal scores (that is, the overall distance of an optimal consensus permutation). Our fixed-parameter algorithms employ the parameters "score of the consensus", "maximum distance between two input permutations", and "number of candidates". We extend our results to votes with ties and incomplete votes, thus, in both cases having no longer permutations as input.