A Simple Reduction for Full-Permuted Pattern Matching Problems on Multi-Track Strings [article]

Carl Barton, Ewan Birney, Tomas Fitzgerald
2019 arXiv   pre-print
In this paper we study a variant of string pattern matching which deals with tuples of strings known as multi-track strings. Multi-track strings are a generalisation of strings (or single-track strings) that have primarily found uses in problems related to searching multiple genomes and music information retrieval. A multi-track string T = (t_1, t_2, t_3, ... , t_N) of length n and track count N is a multi-set of N strings of length n with characters drawn from a common alphabet of size σ_U.
more » ... en two multi-track strings T = (t_1, t_2, t_3, ... , t_N) and P = (p_1, p_2, p_3, ... , p_N) of length n and track count N, there is a full-permuted-match between P and T if t_r_i = p_i for all i ∈{1,2,3,... N } and some permutation (r_1, r_2, r_3...,r_N) of (1, 2, 3,...,N), we denote this PT. Efficient algorithms for some full-permuted-match problems on multi-track strings have recently been presented. In this paper we show a reduction from a multi-track string of length n and track count N with alphabet size σ_U, to a single-track string of length 2n-1 with alphabet size σ_U^N. Through this reduction we allow any string algorithm to be used on multi-track string problems using as the match relation. For polynomial time algorithms on single-track strings of length n there is a multiplicative penalty of not more than O(N)-time for the same algorithm on mt-strings of length n and track count N.
arXiv:1909.02364v5 fatcat:c5somhivc5eglkpa2bj5bbblry