Longest Common Separable Pattern between Permutations

In 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 √ Opt (where Opt is the size of an optimal solution) when taking common patterns belonging to pattern-avoiding classes of permutations.

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Mathilde Bouvel, Dominique Rossin, Stéphane Vialette
• Keywords: Common Separable Pattern, CORR 2007, Education, Input Permutations, Permutations