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DOI: 10.4230/LIPIcs.WABI.2024.14

A Unifying Taxonomy of Pattern Matching in Degenerate Strings and Founder Graphs

Authors: Rocco Ascone, Giulia Bernardini, Alessio Conte, Massimo Equi, Esteban Gabory, Roberto Grossi, and Nadia Pisanti

Published in: LIPIcs, Volume 312, 24th International Workshop on Algorithms in Bioinformatics (WABI 2024)

Abstract

Elastic Degenerate (ED) strings and Elastic Founder (EF) graphs are two versions of acyclic components of pangenomes. Both ED strings and EF graphs (which we collectively name variable strings) extend the well-known notion of indeterminate string. Recent work has extensively investigated algorithmic tasks over these structures, and over several other variable strings notions that they generalise. Among such tasks, the basic operation of matching a pattern into a text, which can serve as a toolkit for many pangenomic data analyses using these data structures, deserves special attention. In this paper we: (1) highlight a clear taxonomy within both ED strings and EF graphs ranging through variable strings of all types, from the linear string up to the most general one; (2) investigate the problem PvarT(X,Y) of matching a solid or variable pattern of type X into a variable text of type Y; (3) using as a reference the quadratic conditional lower bounds that are known for PvarT(solid,ED) and PvarT(solid,EF), for all possible types of variable strings X and Y we either prove the quadratic conditional lower bound for PvarT(X,Y), or provide non-trivial, often sub-quadratic, upper bounds, also exploiting the above-mentioned taxonomy.

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Rocco Ascone, Giulia Bernardini, Alessio Conte, Massimo Equi, Esteban Gabory, Roberto Grossi, and Nadia Pisanti. A Unifying Taxonomy of Pattern Matching in Degenerate Strings and Founder Graphs. In 24th International Workshop on Algorithms in Bioinformatics (WABI 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 312, pp. 14:1-14:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ascone_et_al:LIPIcs.WABI.2024.14,
  author =	{Ascone, Rocco and Bernardini, Giulia and Conte, Alessio and Equi, Massimo and Gabory, Esteban and Grossi, Roberto and Pisanti, Nadia},
  title =	{{A Unifying Taxonomy of Pattern Matching in Degenerate Strings and Founder Graphs}},
  booktitle =	{24th International Workshop on Algorithms in Bioinformatics (WABI 2024)},
  pages =	{14:1--14:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-340-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{312},
  editor =	{Pissis, Solon P. and Sung, Wing-Kin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2024.14},
  URN =		{urn:nbn:de:0030-drops-206586},
  doi =		{10.4230/LIPIcs.WABI.2024.14},
  annote =	{Keywords: Pangenomics, pattern matching, degenerate string, founder graph, fine-grained complexity}
}

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A Unifying Taxonomy of Pattern Matching in Degenerate Strings and Founder Graphs

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