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Finding maximal exact matches in graphs

ALGORITHMS FOR MOLECULAR BIOLOGY 2024年第1期19卷 10页

作者： Rizzo, Nicola Caceres, Manuel Makinen, Veli Univ Helsinki Dept Comp Sci Pietari Kalmin katu 5POB 68 Helsinki 00014 Finland

BackgroundWe 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 kappa\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa$$\end{document} (kappa\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa$$\end{document}-MEMs). However, on arbitrary input graphs, the problem of finding MEMs cannot be solved in truly sub-quadratic time under SETH (Equi et al., TALG 2023) even on acyclic *** this paper we show an O(n center dot L center dot dL-1+m+M kappa,L)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n\cdot L \cdot d<^>{L-1} + m + M_{\kappa ,L})$$\end{document}-time algorithm finding all kappa\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa$$\end{document}-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|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}

关键词： sequence to graph alignment Bidirectional BWT r-index Suffix tree Founder graphs

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Chaining of Maximal Exact Matches in graphs 30th

Chaining of Maximal Exact Matches in Graphs

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30th International Symposium on String Processing and Information Retrieval (SPIRE) / 18th Workshop on Compression, Text, and Algorithms (WCTA)

作者： Rizzo, Nicola Caceres, Manuel Makinen, Veli Univ Helsinki Dept Comp Sci POB 68Pietari Kalmin Katu 5 Helsinki 00014 Finland

ISBN: (纸本)9783031439797;9783031439803

We show how to chain maximal exact matches (MEMs) between a query string Q and a labeled directed acyclic graph (DAG) G = (V, E) to solve the longest common subsequence (LCS) problem between Q and G. We obtain our result via a new symmetric formulation of chaining in DAGs that we solve in O(m + n + k(2)|V| + |E| + kN log N) time, where m = |Q|, n is the total length of node labels, k is the minimum number of paths covering the nodes of G and N is the number of MEMs between Q and node labels, which we show encode full MEMs.

关键词： sequence to graph alignment longest common subsequence sparse dynamic programming

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