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We describe an algorithm to find maximal exact matches (MEMs) among HiFireads with homopolymer errors. The main novelty in our work is that we resortto run-length compression to help deal with errors. Our method receives asinput a run-length-encoded string collection containing the HiFi reads alongwith their reverse complements. Subsequently, it splits the encoding into twoarrays, one storing the sequence of symbols for equal-symbol runs and anotherstoring the run lengths. The purpose of the split is to get the BWT of the runsymbols and reorder their lengths accordingly. We show that this special BWT,as it encodes the HiFi reads and their reverse complements, supportsbi-directional queries for the HiFi reads. Then, we propose a variation of theMEM algorithm of Belazzougui et al. (2013) that exploits the run-lengthencoding and the implicit bi-directional property of our BWT to computeapproximate MEMs. Concretely, if the algorithm finds that two substrings, $a_1\ldots a_p$ and $b_1 \ldots b_p$, have a MEM, then it reports the MEM only iftheir corresponding length sequences, $\ell^{a}_1 \ldots \ell^{a}_p$ and$\ell^{b}_1 \ldots \ell^{b}_p$, do not differ beyond an input threshold. We usea simple metric to calculate the similarity of the length sequences that wecall the {\em run-length excess}. Our technique facilitates the detection ofMEMs with homopolymer errors as it does not require dynamic programming to findapproximate matches where the only edits are the lengths of the equal-symbolruns. Finally, we present a method that relies on a geometric data structure toreport the text occurrences of the MEMs detected by our algorithm.

Computing all-vs-all MEMs in run-length encoded collections of HiFi reads