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Computing matching statistics on Wheeler DFAs.

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This study generalizes matching statistics algorithms for approximate string matching from strings to Wheeler automata. It introduces a longest common prefix (LCP) array for automata, extending compressed suffix tree functionalities to labeled graphs.

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Area of Science:

  • Computer Science
  • Bioinformatics Algorithms
  • Graph Theory

Background:

  • Approximate string matching is crucial in bioinformatics, often solved using matching statistics.
  • Existing efficient algorithms for matching statistics leverage compressed suffix trees and the longest common prefix (LCP) array.
  • These methods are primarily designed for linear string data structures.

Purpose of the Study:

  • To generalize efficient matching statistics algorithms beyond linear strings.
  • To extend the applicability of compressed suffix tree concepts to more complex data structures.
  • To establish foundational methods for analyzing Wheeler automata in the context of string matching.

Main Methods:

  • Generalization of the Ohlebusch et al. (2010) matching statistics algorithm.
  • Adaptation of compressed suffix tree components, specifically the LCP array concept.
  • Development of a novel LCP array definition for Wheeler deterministic finite automata.

Main Results:

  • Successful generalization of matching statistics computation to Wheeler automata.
  • Introduction and formalization of the LCP array concept for Wheeler automata.
  • Demonstration of a pathway to extend suffix tree functionalities to labeled graphs.

Conclusions:

  • The proposed generalization significantly broadens the scope of matching statistics.
  • The LCP array for Wheeler automata is a key innovation for graph-based string processing.
  • This work provides a foundation for advanced bioinformatics algorithms on labeled graphs.