Longest Common Separable Pattern Among Permutations

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In this paper, we study the problem of finding the longest common separable pattern among several permutations. We first give a polynomial-time algorithm when the number of input permutations is fixed and next show that the problem is NP–hardfor an arbitrary number of input permutations even if these permutations are separable.

On the other hand, we show that the NP–hardproblem of finding the longest common pattern between two permutations cannot be approximated better than within a ratio of (where is the size of an optimal solution) when taking common patterns belonging to pattern-avoiding permutation classes.