Finding Pattern Matchings for Permutations

Abstract Given a permutation P of {1,…, k } and T of {1,…, n }, k ⩽ n , 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 finding 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.