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.2020.27
URN: urn:nbn:de:0030-drops-121523
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12152/
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Pape-Lange, Julian

On Extensions of Maximal Repeats in Compressed Strings

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LIPIcs-CPM-2020-27.pdf (0.4 MB)

Abstract

This paper provides upper bounds for several subsets of maximal repeats and maximal pairs in compressed strings and also presents a formerly unknown relationship between maximal pairs and the run-length Burrows-Wheeler transform.
This relationship is used to obtain a different proof for the Burrows-Wheeler conjecture which has recently been proven by Kempa and Kociumaka in "Resolution of the Burrows-Wheeler Transform Conjecture".
More formally, this paper proves that the run-length Burrows-Wheeler transform of a string S with z_S LZ77-factors has at most 73(log₂ |S|)(z_S+2)² runs, and if S does not contain q-th powers, the number of arcs in the compacted directed acyclic word graph of S is bounded from above by 18q(1+log_q |S|)(z_S+2)².

BibTeX - Entry

@InProceedings{papelange:LIPIcs:2020:12152,
  author =	{Julian Pape-Lange},
  title =	{{On Extensions of Maximal Repeats in Compressed Strings}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{27:1--27:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{Inge Li G{\o}rtz and Oren Weimann},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12152},
  URN =		{urn:nbn:de:0030-drops-121523},
  doi =		{10.4230/LIPIcs.CPM.2020.27},
  annote =	{Keywords: Maximal repeats, Extensions of maximal repeats, Combinatorics on compressed strings, LZ77, Burrows-Wheeler transform, Burrows-Wheeler transform conjecture, Compact suffix automata, CDAWGs}
}

Keywords: Maximal repeats, Extensions of maximal repeats, Combinatorics on compressed strings, LZ77, Burrows-Wheeler transform, Burrows-Wheeler transform conjecture, Compact suffix automata, CDAWGs
Collection: 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)
Issue Date: 2020
Date of publication: 09.06.2020

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