Computing Maximal Unique Matches with the r-Index

Authors Sara Giuliani , Giuseppe Romana , Massimiliano Rossi

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Author Details

Sara Giuliani
  • Department of Computer Science, University of Verona, Italy
Giuseppe Romana
  • Department of Computer Science, University of Palermo, Italy
Massimiliano Rossi
  • Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL, USA


We thank Travis Gagie for suggesting this problem as a project for his course CSCI 6905 at Dalhousie University. We also thank the anonymous reviewers for their insightful comments.

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Sara Giuliani, Giuseppe Romana, and Massimiliano Rossi. Computing Maximal Unique Matches with the r-Index. In 20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 22:1-22:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
  • Burrows-Wheeler Transform
  • r-index
  • maximal unique matches
  • bioinformatics
  • pangenomics


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