The Complexity of Pattern Matching for 321-Avoiding and Skew-Merged Permutations.

The PERMUTATION PATTERN MATCHING problem, asking whether a pattern permutation pi is contained in a text permutation tau, is known to be NP-complete. We present two polynomial time algorithms for special cases. The first is applicable if both pi and tau are 321-avoiding while the second is applicable if both permutations are skew-merged. Both algorithms have a runtime of O (kn), where k is the length of pi and n the length of tau.