KMP Based Pattern Matching Algorithms for Multi-Track Strings

Multi-track string is an N -tuple strings of length n. For two multi-track strings T = (t1, t2, . . . , tN ) of length n and P = (p1, p2, ..., pM ) of length m, permuted pattern matching is a problem to find all positions i such that P is permuted match with T[i : i+M ]. We propose three new algorithms for permuted pattern matching based on the KMP algorithm. The first algorithm is an exact matching algorithm that runs in O(nN) time after O(mM)-time preprocessing. The second and third algorithms are filtering algorithms that run in O(n(N + σ)) after O(m(M + σ))time preprocessing, where σ is the size of alphabet. Experiments show that our algorithms run faster than AC automaton based algorithm that proposed by Katsura et al. [5].