License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CPM.2017.1
URN: urn:nbn:de:0030-drops-73343
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Manzini, Giovanni

Wheeler Graphs: Variations on a Theme by Burrows and Wheeler

LIPIcs-CPM-2017-1.pdf (0.2 MB)


The famous Burrows-Wheeler Transform was originally defined for single strings but variations have been developed for sets of strings, labelled trees, de Bruijn graphs, alignments, etc. In this talk we propose a unifying view that includes many of these variations and that we hope will simplify the search for more.

Somewhat surprisingly we get our unifying view by considering the Nondeterministic Finite Automata related to different pattern-matching problems. We show that the state graphs associated with these automata have common properties that we summarize with the concept of a Wheeler graph. Using the notion of a Wheeler graph, we show that it is possible to process strings efficiently even if the automaton is nondeterministic. In addition, we show that Wheeler graphs can be compactly represented and traversed using up to three arrays with additional data structures supporting efficient rank and select operations. It turns out that these arrays coincide with, or are substantially equivalent to, the output of many Burrows-Wheeler Transform variants described in the literature.

This is joint work with Travis Gagie and Jouni Sirén.

BibTeX - Entry

  author =	{Giovanni Manzini},
  title =	{{Wheeler Graphs: Variations on a Theme by Burrows and Wheeler}},
  booktitle =	{28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)},
  pages =	{1:1--1:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-039-2},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{78},
  editor =	{Juha K{\"a}rkk{\"a}inen and Jakub Radoszewski and Wojciech Rytter},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-73343},
  doi =		{10.4230/LIPIcs.CPM.2017.1},
  annote =	{Keywords: compressed data structures, pattern matching}

Keywords: compressed data structures, pattern matching
Collection: 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)
Issue Date: 2017
Date of publication: 30.06.2017

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