Recently, Gagie et al. proposed a version of the FM-index, called the r-index, that can store thousands of human genomes on a commodity computer. Then Kuhnle et al. showed how to build the r-index efficiently via a technique called prefix-free parsing (PFP) and demonstrated its effectiveness for exact pattern matching. Exact pattern matching can be leveraged to support approximate pattern matching, but the r-index itself cannot support efficiently popular and important queries such as finding maximal exact matches (MEMs). To address this shortcoming, Bannai et al. introduced the concept of thresholds, and showed that storing them together with the r-index enables efficient MEM finding-but they did not say how to find those thresholds. We present a novel algorithm that applies PFP to build the r-index and find the thresholds simultaneously and in linear time and space with respect to the size of the prefix-free parse. Our implementation called can rapidly find MEMs between reads and large-sequence collections of highly repetitive sequences. Compared with other read aligners-PuffAligner, Bowtie2, BWA-MEM, and CHIC- MONI used 2-11 times less memory and was 2-32 times faster for index construction. Moreover, MONI was less than one thousandth the size of competing indexes for large collections of human chromosomes. Thus, MONI represents a major advance in our ability to perform MEM finding against very large collections of related references.
Keywords: MEM-finding; r-index; run-length-encoded Burrows-Wheeler transform; thresholds.