Fast full permuted pattern matching algorithms on multi-track strings

A multi-track string is a tuple of strings of the same length. The full permuted pattern matching problem is, given two multi-track strings T = (t1, t2, . . . , tN) and P = (p1, p2, . . . , pN) such that |p1| = = |pN| ≤ |t1| = = |tN|, to find all positions i such that P = (tr1 [i : I+m-1], . . . , trN [i : I+m-1]) for some permutation (r1, . . . , rN) of (1, . . . ,N), where m = |p1| and t[i : J] denotes the substring of t from position i to j. We propose new algorithms that perform full permuted pattern matching practically fast. The first and second algorithms are based on the Boyer-Moore algorithm and the Horspool algorithm, respectively. The third algorithm is based on the Aho-Corasick algorithm where we use a multi-track character instead of a single character in the so-called goto function. The fourth algorithm is an improvement of the multi-track Knuth-Morris-Pratt algorithm that uses an automaton instead of the failure function of the original algorithm. Our experiment results demonstrate that those algorithms perform permuted pattern matching faster than existing algorithms.