Fixed-Parameter Algorithms for Kemeny Scores

The Kemeny Score problem 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 fixedparameter 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.

• Type: Conference
• Year: 2008
• Where: AAIM
• Authors: Nadja Betzler, Michael R. Fellows, Jiong Guo, Rolf Niedermeier, Frances A. Rosamond
• Keywords: AAIM 2008, Algorithms, Consensus Permutation, Optimal Consensus Permutation, Permutations