The distance of a permutation from a subgroup of Sn
Richard G. E. Pinch
Abstract
We show that the problem of computing the distance of a given permutation from a subgroup H of Sn 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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