Longest Common Separable Pattern Among Permutations

  • Mathilde Bouvel
  • Dominique Rossin
  • Stéphane Vialette
Conference paper

DOI: 10.1007/978-3-540-73437-6_32

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4580)
Cite this paper as:
Bouvel M., Rossin D., Vialette S. (2007) Longest Common Separable Pattern Among Permutations. In: Ma B., Zhang K. (eds) Combinatorial Pattern Matching. CPM 2007. Lecture Notes in Computer Science, vol 4580. Springer, Berlin, Heidelberg

Abstract

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 Open image in new window (where Open image in new window is the size of an optimal solution) when taking common patterns belonging to pattern-avoiding permutation classes.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Mathilde Bouvel
    • 1
  • Dominique Rossin
    • 1
  • Stéphane Vialette
    • 2
  1. 1.CNRS, Université Paris Diderot, Laboratoire d’Informatique Algorithmique: Fondements et Applications, 2 Place Jussieu, Case 7014, F-75251 Paris Cedex 05France
  2. 2.Laboratoire de Recherche en Informatique (LRI), bât.490, Univ. Paris-Sud XI, F-91405 Orsay cedexFrance

Personalised recommendations