Pattern matching for 321-avoiding permutations

Abstract

Given two permutations π and σ, the NP-complete Permutation Pattern problem is to decide whether π contains σ as a pattern. In case both π and σ are 321-avoiding, we prove the Permutation Pattern problem to be solvable in O(k 2 n 6) time, where k=|σ| and n=|π|, and give a time algorithm if only σ is 321-avoiding. Finally, we show W[1]-hardness of a 2-colored version of this latter problem. © 2009 Springer-Verlag Berlin Heidelberg.