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Wheeler Graphs and Wheeler Languages

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

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Subject Classification

ACM Subject Classification
  • Theory of computation → Sorting and searching
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Pattern matching
  • Theory of computation → Formal languages and automata theory
Keywords
  • Wheeler languages
  • Wheeler graphs
  • pattern matching
  • indexing
  • compressed data structures

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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.

Cite As Get BibTex

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) https://doi.org/10.4230/OASIcs.Manzini.12

Author Details

Nicola Cotumaccio
  • University of Helsinki, Finland
Giovanna D'Agostino
  • University of Udine, Italy
Daniel Gibney
  • University of Texas at Dallas, TX, USA
Alberto Policriti
  • University of Udine, Italy
Nicola Prezza
  • DAIS, Ca' Foscari University of Venice, Italy
Sharma V. Thankachan
  • North Carolina State University, Raleigh, NC, USA

Funding

  • Cotumaccio, Nicola: Funded by the Helsinki Institute for Information Technology (HIIT).
  • Prezza, Nicola: Funded by the European Union (ERC, REGINDEX, 101039208). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.
  • Thankachan, Sharma V.: Partially supported by NSF under grants CCF-2316691 and CCF-2315822.

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