Longest Common Separable Pattern between Permutations
<|reference_start|>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 $sqrt{Opt}$ (where $Opt$ is the size of an optimal solution) when taking common patterns belonging to pattern-avoiding classes of permutations.<|reference_end|>
@article{bouvel2007longest,
    title={Longest Common Separable Pattern between Permutations},
    author={Mathilde Bouvel (LIAFA), Dominique Rossin (LIAFA), Stephane Vialette
  (LRI)},
    journal={Combinatorial Pattern Matching (CPM) 2007 (2007) 00},
    year={2007},
    archivePrefix={arXiv},
    eprint={math/0702109},
    primaryClass={math.CO cs.CC}
}