Computing All-vs-All MEMs in Run-Length-Encoded Collections of HiFi Reads

Abstract

We describe an algorithm to find maximal exact matches (MEMs) among HiFi reads with homopolymer errors. The main novelty in our work is that we resort to run-length compression to help deal with errors. Our method receives as input a run-length-encoded string collection containing the HiFi reads along with their reverse complements. Subsequently, it splits the encoding into two arrays, one storing the sequence of symbols for equal-symbol runs and another storing the run lengths. The purpose of the split is to get the BWT of the run symbols and reorder their lengths accordingly. We show that this special BWT, as it encodes the HiFi reads and their reverse complements, supports bi-directional queries for the HiFi reads. Then, we propose a variation of the MEM algorithm of Belazzougui et al. (2013) that exploits the run-length encoding and the implicit bi-directional property of our BWT to compute approximate 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 if their 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 use a simple metric to calculate the similarity of the length sequences that we call the run-length excess. Our technique facilitates the detection of MEMs with homopolymer errors as it does not require dynamic programming to find approximate matches where the only edits are the lengths of the equal-symbol runs. Finally, we present a method that relies on a geometric data structure to report the text occurrences of the MEMs detected by our algorithm.

Supported by Academy of Finland Grants 323233 and 339070.

Appendix

Fig. 1.

Reporting MEMs from an internal node v labeled $\textsf{label}(v)=X$ using the grid $\mathcal {G}$. The rows are labeled with the suffixes prefixed by X, while the column are labeled with the suffixes prefixed with the labels of v’s Weiner links. The horizontal red lines represents the partition of the $S\!A$ range for X induced by the children of v. The grey numbers below the column labels are the $\textsf{LF}^{-1}$ values. For each column $j'$, its associated $S\!A$ value is in the row $\textsf{LF}^{-1}(j')=j$.