The complexity of pattern matching for 321-avoiding and skew-merged permutations

Abstract

The PERMUTATION PATTERN MATCHING problem, asking whether a pattern permutation π is contained in a text permutation τ, is known to be NP-complete. We present two polynomial time algorithms for special cases. The first is applicable if both π and τ 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 π and n the length of τ.