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Faster Longest Common Extension Queries in Strings over General Alphabets

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Abstract

Longest common extension queries (often called longest common prefix queries) constitute a fundamental building block in multiple string algorithms, for example computing runs and approximate pattern matching. We show that a sequence of q LCE queries for a string of size n over a general ordered alphabet can be realized in O(q log log n + n log* n) time making only O(q + n) symbol comparisons. Consequently, all runs in a string over a general ordered alphabets can be computed in O(n log log n) time making O(n) symbol comparisons. Our results improve upon a solution by Kosolobov (Information Processing Letters, 2016), who designed an algorithm with O(n log^⅔ n) running time and conjectured that O(n) time is possible. Our paper makes a significant progress towards resolving this conjecture. Our techniques extend to the case of general unordered alphabets, when the time increases to O(q log n + n log* n). The main tools are difference covers and a variant of the disjoint-sets data structure by La Poutré (SODA 1990).

BibTeX - Entry

@InProceedings{gawrychowski_et_al:LIPIcs:2016:6081,
  author =	{Pawel Gawrychowski and Tomasz Kociumaka and Wojciech Rytter and Tomasz Walen},
  title =	{{Faster Longest Common Extension Queries in Strings over General Alphabets}},
  booktitle =	{27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)},
  pages =	{5:1--5:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-012-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{54},
  editor =	{Roberto Grossi and Moshe Lewenstein},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6081},
  URN =		{urn:nbn:de:0030-drops-60810},
  doi =		{10.4230/LIPIcs.CPM.2016.5},
  annote =	{Keywords: longest common extension, longest common prefix, maximal repetitions, difference cover}
}

Keywords: longest common extension, longest common prefix, maximal repetitions, difference cover
Seminar: 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)
Issue date: 2016
Date of publication: 2016


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