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The NP-complete Permutation Pattern Matching problem asks whether apermutation P (the pattern) can be matched into a permutation T (the text). Amatching is an order-preserving embedding of P into T. In the GeneralizedPermutation Pattern Matching problem one can additionally enforce that certainadjacent elements in the pattern must be mapped to adjacent elements in thetext. This paper studies the parameterized complexity of this more generalproblem. We show W[1]-completeness with respect to the length of the pattern P.Under standard complexity theoretic assumptions this implies that nofixed-parameter tractable algorithm can be found for any parameter dependingsolely on P.

A W[1]-Completeness Result for Generalized Permutation Pattern Matching