Longest Common Pattern between two Permutations
  In this paper, we give a polynomial (O(n^8)) algorithm for finding a longest common pattern between two permutations of size n given that one is separable. We also give an algorithm for general permutations whose complexity depends on the length of the longest simple permutation involved in one of our permutations. 
Dominique Rossin (LIAFA), Mathilde Bouvel (LIAFA)