Computing Matching Statistics on Repetitive Texts

Computing the {\em matching statistics} of a string $P[1..m]$ with respect to a text $T[1..n]$ is a fundamental problem which has application to genome sequence comparison. In this paper, we study the problem of computing the matching statistics upon highly repetitive texts. We design three different data structures that are similar to LZ-compressed indexes. The space costs of all of them can be measured by $\gamma$, the size of the smallest string attractor [STOC'2018] and $\delta$, a better measure of repetitiveness [LATIN'2020].