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;⋯; t_N) of length n and ℙ = (p₁; p₂; ⋯, p_M) 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].