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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 , Nadia Pisanti

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Author Details

Rocco Ascone
  • University of Trieste, Italy
Giulia Bernardini
  • University of Trieste, Italy
Alessio Conte
  • University of Pisa, Italy
Massimo Equi
  • University of Helsinki, Finland
Esteban Gabory
  • CWI, Amsterdam, The Netherlands
Roberto Grossi
  • University of Pisa, Italy
Nadia Pisanti
  • University of Pisa, Italy

Funding

This work was partially supported by the PANGAIA (RG and NP) and ALPACA (EG and NP) projects that received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreements No. 872539 and 956229, respectively. RG and NP were partially supported by NextGeneration EU programme PNRR ECS00000017 Tuscany Health Ecosystem.
  • Bernardini, Giulia: GB is a member of the Gruppo Nazionale Calcolo Scientifico-Istituto Nazionale di Alta Matematica (GNCS-INdAM) and was supported by the MUR - FSE REACT EU - PON R&I 2014-2020.
  • Equi, Massimo: ME was funded by the Helsinki Institute for Information Technology (HIIT).
  • Pisanti, Nadia: NP was partially supported by MUR PRIN 2022 YRB97K PINC.

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.WABI.2024.14

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
  • Theory of computation → Problems, reductions and completeness
  • Applied computing → Molecular sequence analysis
  • Applied computing → Computational genomics
Keywords
  • Pangenomics
  • pattern matching
  • degenerate string
  • founder graph
  • fine-grained complexity

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