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Published in:
2007 | OriginalPaper | Chapter
Longest Common Separable Pattern Among Permutations
Authors : Mathilde Bouvel, Dominique Rossin, Stéphane Vialette
Published in: Combinatorial Pattern Matching
Publisher: Springer Berlin Heidelberg
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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
(where
is the size of an optimal solution) when taking common patterns belonging to pattern-avoiding permutation classes.