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Finding Maximal Exact Matches in Graphs

Authors Nicola Rizzo , Manuel Cáceres , Veli Mäkinen

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Author Details

Nicola Rizzo
  • Department of Computer Science, University of Helsinki, Finland
Manuel Cáceres
  • Department of Computer Science, University of Helsinki, Finland
Veli Mäkinen
  • Department of Computer Science, University of Helsinki, Finland

Funding

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 956229, and from the Academy of Finland grants No. 352821 and 328877.

Acknowledgements

We thank an anonymous reviewer for pointing out an anomaly that lead us to correct the choice of a parameter value in our experiments.

Cite AsGet BibTex

Nicola Rizzo, Manuel Cáceres, and Veli Mäkinen. Finding Maximal Exact Matches in Graphs. In 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 273, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.WABI.2023.10

Abstract

We study the problem of finding maximal exact matches (MEMs) between a query string Q and a labeled graph G. MEMs are an important class of seeds, often used in seed-chain-extend type of practical alignment methods because of their strong connections to classical metrics. A principled way to speed up chaining is to limit the number of MEMs by considering only MEMs of length at least κ (κ-MEMs). However, on arbitrary input graphs, the problem of finding MEMs cannot be solved in truly sub-quadratic time under SETH (Equi et al., ICALP 2019) even on acyclic graphs. In this paper we show an O(n⋅ L ⋅ d^{L-1} + m + M_{κ,L})-time algorithm finding all κ-MEMs between Q and G spanning exactly L nodes in G, where n is the total length of node labels, d is the maximum degree of a node in G, m = |Q|, and M_{κ,L} is the number of output MEMs. We use this algorithm to develop a κ-MEM finding solution on indexable Elastic Founder Graphs (Equi et al., Algorithmica 2022) running in time O(nH² + m + M_κ), where H is the maximum number of nodes in a block, and M_κ is the total number of κ-MEMs. Our results generalize to the analysis of multiple query strings (MEMs between G and any of the strings). Additionally, we provide some preliminary experimental results showing that the number of graph MEMs is an order of magnitude smaller than the number of string MEMs of the corresponding concatenated collection.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Pattern matching
  • Theory of computation → Sorting and searching
  • Applied computing → Genomics
Keywords
  • Sequence to graph alignment
  • bidirectional BWT
  • r-index
  • suffix tree
  • founder graphs

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