  In recent years, pangenomes received increasing attention from the scientific
community for their ability to incorporate population variation information and
alleviate reference genome bias. Maximal Exact Matches (MEMs) and Maximal
Unique Matches (MUMs) have proven themselves to be useful in multiple
bioinformatic contexts, for example short-read alignment and multiple-genome
alignment. However, standard techniques using suffix trees and FM-indexes do
not scale to a pangenomic level. Recently, Gagie et al. [JACM 20] introduced
the $r$-index that is a Burrows-Wheeler Transform (BWT)-based index able to
handle hundreds of human genomes. Later, Rossi et al. [JCB 22] enabled the
computation of MEMs using the $r$-index, and Boucher et al. [DCC 21] showed how
to compute them in a streaming fashion. In this paper, we show how to augment
Boucher et al.'s approach to enable the computation of MUMs on the $r$-index,
while preserving the space and time bounds. We add additional $O(r)$ samples of
the longest common prefix (LCP) array, where $r$ is the number of equal-letter
runs of the BWT, that permits the computation of the second longest match of
the pattern suffix with respect to the input text, which in turn allows the
computation of candidate MUMs. We implemented a proof-of-concept of our
approach, that we call mum-phinder, and tested on real-world datasets. We
compared our approach with competing methods that are able to compute MUMs. We
observe that our method is up to 8 times smaller, while up to 19 times slower
when the dataset is not highly repetitive, while on highly repetitive data, our
method is up to 6.5 times slower and uses up to 25 times less memory.
