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Wheeler Graphs and Wheeler Languages

Authors: Nicola Cotumaccio, Giovanna D'Agostino, Daniel Gibney, Alberto Policriti, Nicola Prezza, and Sharma V. Thankachan

Published in: OASIcs, Volume 131, The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday (2025)

Abstract

Suffix sorting stands at the core of the most efficient solutions for indexed pattern matching: the suffix tree, the suffix array, compressed indexes based on the Burrows-Wheeler transform, and so on. In [Gagie, Manzini, Sirén, TCS 2017] this concept was extended to labeled graphs, obtaining the rich class of Wheeler graphs. This work opened a very fruitful line of research, ultimately generating results able to bridge the fields of compressed data structures, graph theory, and regular language theory. In a Wheeler graph, nodes are sorted according to the alphabetic order of their incoming labels, propagating this order through pairs of equally-labeled edges. This apparently-simple definition makes it possible to solve on Wheeler graphs problems (including, but not limited to: compression, subpath queries, NFA equivalence, determinization, minimization) that on general labeled graphs are extremely hard to solve, and induces a rich structure in the class of regular languages (Wheeler languages) recognized by automata whose state transition is a Wheeler graph. The goal of this survey is to provide a summary of (and intuitions behind) the results on Wheeler graphs that appeared in the literature since their introduction, in addition to a discussion of interesting problems that are still open in the field.

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Nicola Cotumaccio, Giovanna D'Agostino, Daniel Gibney, Alberto Policriti, Nicola Prezza, and Sharma V. Thankachan. Wheeler Graphs and Wheeler Languages. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 12:1-12:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cotumaccio_et_al:OASIcs.Manzini.12,
  author =	{Cotumaccio, Nicola and D'Agostino, Giovanna and Gibney, Daniel and Policriti, Alberto and Prezza, Nicola and Thankachan, Sharma V.},
  title =	{{Wheeler Graphs and Wheeler Languages}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{12:1--12:28},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-390-4},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{131},
  editor =	{Ferragina, Paolo and Gagie, Travis and Navarro, Gonzalo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Manzini.12},
  URN =		{urn:nbn:de:0030-drops-239205},
  doi =		{10.4230/OASIcs.Manzini.12},
  annote =	{Keywords: Wheeler languages, Wheeler graphs, pattern matching, indexing, compressed data structures}
}

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Wheeler Graphs and Wheeler Languages

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