Position heaps for permuted pattern matching on multi-track strings

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,⋯, t_N} of length n and ℙ = {p₁,⋯, pN} of length m, outputs all positions i such that {p1,⋯,pN} = {t₁[i: i + m - 1],⋯, t_N [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(m² N + 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(m² N² + occ) time. We show that both of them can be constructed in O(nN) time.