Abstract
The median of permutations problem consists in finding a consensus permutation of a given set of m permutations of size n. This consensus represent the “closest” permutation to the given set under the Kendall-tau distance. Since the complexity of this problem is still unknown for sets of 3 permutations, in the following work, we investigate this specific case and show an interesting link with the 3-Hitting Set problem.
Supported by NSERC through an Individual Discovery Grant (Hamel), by FRQNT through a Ph.D’s scholarship and Mitacs through a Globalink Research Award (Milosz).
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Acknowledgements
Thanks to Sarah Cohen-Boulakia, Alain Denise and Pierre Andrieu from the bioinformatic team of Laboratoire de Recherche Informatique of Université Paris-Sud for useful advices and thoughts. Thanks to Mitacs which made this collaboration possible through a Mitacs Globalink grant.
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Milosz, R., Hamel, S., Pierrot, A. (2018). Median of 3 Permutations, 3-Cycles and 3-Hitting Set Problem. In: Iliopoulos, C., Leong, H., Sung, WK. (eds) Combinatorial Algorithms. IWOCA 2018. Lecture Notes in Computer Science(), vol 10979. Springer, Cham. https://doi.org/10.1007/978-3-319-94667-2_19
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