Median Of 3 Permutations, 3-Cycles And 3-Hitting Set Problem

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.