2011/09/09 by Marie-Louise Bruner, Bruner, Marie-Louise, Martin Lackner +1
Computer Science · Mathematics · #68Q25 #Combinatorics (math.CO) #Computational Complexity (cs.CC) #F.2.2 #FOS: Computer and information sciences #FOS: Mathematics #acm:68Q25 #cs.CC #math.CO #msc:68Q25
paper · pdf · doi:10.48550/arxiv.1109.1951
The contents of this paper have been integrated in the more comprehensive paper "The computational landscape of permutation patterns", arXiv:1301.0340
arxiv created 2013/01/14 · arxiv updated 2013/01/15
The NP-complete Permutation Pattern Matching problem asks whether a permutation P (the pattern) can be matched into a permutation T (the text). A matching is an order-preserving embedding of P into T. In the Generalized Permutation Pattern Matching problem one can additionally enforce that certain adjacent elements in the pattern must be mapped to adjacent elements in the text. This paper studies the parameterized complexity of this more general problem. We show W[1]-completeness with respect to the length of the pattern P. Under standard complexity theoretic assumptions this implies that no fixed-parameter tractable algorithm can be found for any parameter depending solely on P.