Information Processing Letters
Generating trees and the Catalan and Schro¨der numbers
Discrete Mathematics
Finding pattern matchings for permutations
Information Processing Letters
Pattern matching for permutations
Information Processing Letters
Permutations, parenthesis words, and Schro¨der numbers
Discrete Mathematics
The Complexity of Some Problems on Subsequences and Supersequences
Journal of the ACM (JACM)
Introduction to algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Algorithms for Pattern Involvement in Permutations
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Excluded permutation matrices and the Stanley-Wilf conjecture
Journal of Combinatorial Theory Series A
Perfect Sorting by Reversals Is Not Always Difficult
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Approximation of RNA multiple structural alignment
CPM'06 Proceedings of the 17th Annual conference on Combinatorial Pattern Matching
Computing common intervals of K permutations, with applications to modular decomposition of graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Revisiting t. uno and m. yagiura's algorithm
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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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-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 patternavoiding permutation classes.