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The distance of a permutation from a subgroup of S_n

Richard G. E. Pinch
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Abstract

We show that the problem of computing the distance of a given permutation from a subgroup $H$ of $S_n$ is in general NP-complete, even under the restriction that $H$ is elementary Abelian of exponent 2. The problem is shown to be polynomial-time equivalent to a problem related to finding a maximal partition of the edges of an Eulerian directed graph into cycles and this problem is in turn equivalent to the standard NP-complete problem of Boolean satisfiability.

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Richard G. E. Pinch. 2005-11-20. The distance of a permutation from a subgroup of S_n. https://arxiv.org/abs/math/0511501

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