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Travis Gagie1, Giovanni Manzini2,3, Jouni Sirén4

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Summary
This summary is machine-generated.

This paper introduces Wheeler graphs, a framework simplifying variations of the Burrows-Wheeler Transform (BWT). Wheeler graphs enable compact storage and fast processing of non-deterministic finite-state automata through path coherence.

Keywords:
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Area of Science:

  • Computer Science
  • Data Structures
  • Algorithms

Background:

  • The Burrows-Wheeler Transform (BWT) is a data-sorting algorithm with applications in data compression.
  • Existing BWT variations are tailored for specific data structures like trees and graphs.
  • A unified framework is needed to encompass and extend BWT applications.

Purpose of the Study:

  • To propose a novel framework, Wheeler graphs, unifying existing BWT variations.
  • To introduce and define the property of path coherence in Wheeler graphs.
  • To demonstrate the utility of Wheeler graphs in efficiently representing and processing non-deterministic finite-state automata.

Main Methods:

  • Definition of Wheeler graphs and their path coherence property.
  • Construction of finite-state automata for various BWT-related problems.
  • Analysis of state diagrams to confirm they are Wheeler graphs.

Main Results:

  • Wheeler graphs exhibit path coherence, allowing for ordered node representation.
  • This ordering enables compact storage and rapid string processing for non-deterministic automata.
  • Several BWT variations were successfully rederived using the proposed framework.

Conclusions:

  • The Wheeler graph framework provides a unified approach to BWT variations.
  • Path coherence is key to efficient representation of automata.
  • This work simplifies existing BWT algorithms and facilitates the discovery of new ones.