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Permutation Reconstruction from Differences
Marzio De Biasi
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We prove that the problem of reconstructing a permutation π₁,…,πₙ of the integers [1…n] given the absolute differences |πᵢ₊₁-πᵢ|, i = 1,…,n-1 is NP-complete. As an intermediate step we first prove the NP-completeness of the decision version of a new puzzle game that we call Crazy Frog Puzzle. The permutation reconstruction from differences is one of the simplest combinatorial problems that have been proved to be computationally intractable.
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