Position Heaps for Permuted Pattern Matching on Multi-Track String

A multi-set of N strings of length n is called a multi-track string. The permuted pattern matching is the problem that given two multi-track strings T = {t1, . . . , tN} of length n and P = {p1, . . . , pN} of length m, outputs all positions i such that {p1, . . . , pN} = {t1[i : i+m−1], . . . , tN [i : i+m−1]}We propose two new indexing structures for multi-track stings. One is a time-efficient structure for T that needs O(nN) space and enables us to solve the problem in O(mN+occ) time, where occ is the number of occurrences of the pattern P in the text T. The other is memory-efficient, it requires only O(n) space, whereas the matching consumes O(mN + occ) time. We show that both of them can be constructed in O(nN) time.