Longest Common Separable Pattern between Permutations

Mathilde Bouvel (1) , Dominique Rossin (1) , Stéphane Vialette (2)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 Algorithmics

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 $sqrt{Opt}$ (where $Opt$ is the size of an optimal solution) when taking common patterns belonging to pattern-avoiding classes of permutations.

Mots clés: permutation; pattern matching

Domaines: Combinatoire [math.CO]; Complexité [cs.CC]

Mathilde Bouvel, Dominique Rossin, Stéphane Vialette. Longest Common Separable Pattern between Permutations. Combinatorial Pattern Matching, 18th Annual Symposium, CPM 2007, London, Canada, July 9-11, 2007, 2007, London, Canada. pp.316-327. ⟨hal-00128750⟩