Finding Pattern Matchings for Permutations

Given a permutation P of f1; : : : ; kg and T of f1; : : : ; ng, the pattern matching problem for permutations is to determine whether there is a length k subsequence of T whose elements are ordered in the same way as the elements of P . We present an O(kn 4 ) time and O(kn 3 ) space algorithm for nding a match of P into T or determining that no match exists, given that P is separable, i.e. contains neither (2, 4, 1, 3) nor (3, 1, 4, 2) as a subpattern.