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Pattern matching through Chaos Game Representation: bridging numerical and discrete data structures for biological

Susana Vinga1, Alexandra M Carvalho, Alexandre P Francisco

  • 1Instituto de Engenharia de Sistemas e Computadores: Investigação e Desenvolvimento (INESC-ID), R, Alves Redol 9, 1000-029 Lisboa, Portugal. svinga@kdbio.inesc-id.pt.

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Summary

Chaos Game Representation (CGR) offers a unifying mathematical framework for sequence analysis, enabling efficient solutions for string matching problems and providing a constant time solution for longest common extension queries.

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Area of Science:

  • Computational Biology
  • Bioinformatics Algorithms
  • Sequence Analysis

Background:

  • Chaos Game Representation (CGR) maps discrete sequences to a continuous domain for statistical and topological analysis.
  • CGR has been extended beyond genomics to various bioinformatics problems.
  • This study explores CGR's applicability to graph-based algorithms.

Purpose of the Study:

  • To investigate the extension of Chaos Game Representation (CGR) to algorithms utilizing discrete, graph-based representations.
  • To refactor foundational string problems using CGR-based algorithms.
  • To evaluate CGR's potential as a unifying framework for sequence analysis.

Main Methods:

  • Exploratory analysis refactoring foundational string problems with CGR-based algorithms.
  • Demonstrating CGR's ability to emulate suffix trees and solve string matching problems.
  • Analyzing the efficiency of CGR for longest common extension (LCE) queries and its use in the Rabin-Karp algorithm.

Main Results:

  • CGR effectively emulates suffix trees, efficiently solving exact and approximate string matching, including palindrome and tandem repeat finding.
  • Longest Common Extension (LCE) queries are solved in constant time using CGR.
  • CGR can be utilized as a rolling hash function within the Rabin-Karp algorithm.

Conclusions:

  • CGR provides a unifying mathematical framework for sequence analysis, addressing challenges in performance and analytical foundations.
  • CGR enables the derivation of graph-based data structures from numerical CGR maps for sequence analysis operations.
  • CGR promises improved performance and a unified analytical approach for diverse pattern matching problems.