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  3. Pattern Matching With Elastic-degenerate Strings And Elastic-founder Graphs.
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  3. Pattern Matching With Elastic-degenerate Strings And Elastic-founder Graphs.

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Pattern matching with Elastic-Degenerate strings and Elastic-Founder graphs.

Rocco Ascone1, Giulia Bernardini2,3, Alessio Conte4

  • 1University of Trieste, Trieste , Italy.

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|April 29, 2026

View abstract on PubMed

Summary
This summary is machine-generated.

This study introduces a taxonomy for variable strings, including Elastic Degenerate (ED) strings and Elastic Founder (EF) graphs, and analyzes pattern matching algorithms within these structures. Researchers establish time complexity bounds for matching patterns into variable texts, advancing pangenomic data analysis.

Keywords:
Degenerate stringFine-grained complexityFounder graphGenome variantPangenomicsPattern matching

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Area of Science:

  • Bioinformatics
  • Computational Biology
  • Stringology

Background:

  • Pangenomics involves analyzing complex genomic structures beyond linear sequences.
  • Variable strings, such as Elastic Degenerate (ED) strings and Elastic Founder (EF) graphs, are crucial for representing acyclic components of pangenomes.
  • Pattern matching is a fundamental operation in pangenomic data analysis, but its complexity with variable strings is not fully understood.

Purpose of the Study:

  • To establish a comprehensive taxonomy of variable string types, ranging from simple linear strings to complex ED strings and EF graphs.
  • To investigate the time complexity of the MATCH(X,Y) problem, which involves matching patterns of type X into texts of type Y, where X and Y are variable strings.
  • To provide non-trivial upper bounds or prove conditional lower bounds for all combinations of pattern and text types within the established taxonomy.

Main Methods:

  • Development of a clear classification system for variable strings based on their complexity and structure.
  • Systematic analysis of the MATCH(X,Y) problem across all pairs of string types in the taxonomy.
  • Derivation of time complexity bounds, including sub-quadratic upper bounds and quadratic conditional lower bounds, referencing existing results.

Main Results:

  • A taxonomy categorizing variable strings from linear strings to complex ED strings and EF graphs is established.
  • For all pattern (X) and text (Y) combinations, non-trivial time complexity bounds for MATCH(X,Y) are provided.
  • Sub-quadratic upper bounds or quadratic conditional lower bounds are determined for pattern matching within the variable string taxonomy.

Conclusions:

  • The study provides a foundational understanding of pattern matching complexities within various variable string representations relevant to pangenomics.
  • The established bounds offer crucial insights for developing efficient algorithms for pangenomic data analysis.
  • This work advances the algorithmic toolkit for handling complex genomic structures represented by variable strings.