2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131340In this article, we study the problem of finding the longest common separable pattern between several permutations. We give a polynomial-time algorithm when the number of input permutations is fixed and show that the problem is NP-hard for an arbitrary number of input permutations even if these permutations are separable. On the other hand, we show that the NP-hard problem of finding the longest common pattern between two permutations cannot be approximated better than within a ratio of $sqrt{Opt}$ (where $Opt$ is the size of an optimal solution) when taking common patterns belonging to pattern-avoiding classes of permutations.15 pagesCombinatoricsComputational Complexity05A05 - 05C12 - 05C85 - 05C05- 90C39text