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.2016.8
URN: urn:nbn:de:0030-drops-60842
URL: https://drops.dagstuhl.de/opus/volltexte/2016/6084/
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Iliopoulos, Costas S. ; Radoszewski, Jakub

Truly Subquadratic-Time Extension Queries and Periodicity Detection in Strings with Uncertainties

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Abstract

Strings with don't care symbols, also called partial words, and more general indeterminate strings are a natural representation of strings containing uncertain symbols. A considerable effort has been made to obtain efficient algorithms for pattern matching and periodicity detection in such strings. Among those, a number of algorithms have been proposed that behave well on random data, but still their worst-case running time is Theta(n^2). We present the first truly subquadratic-time solutions for a number of such problems on partial words that can also be adapted to indeterminate strings over a constant-sized alphabet. We show that $n$ longest common compatible prefix queries (which correspond to longest common extension queries in regular strings) can be answered on-line in O(n * sqrt(n * log(n)) time after O(n * sqrt(n * log(n))-time preprocessing. We also present O(n * sqrt(n * log(n))-time algorithms for computing the prefix array and two types of border array of a partial word.

BibTeX - Entry

@InProceedings{iliopoulos_et_al:LIPIcs:2016:6084,
  author =	{Costas S. Iliopoulos and Jakub Radoszewski},
  title =	{{Truly Subquadratic-Time Extension Queries and Periodicity Detection in Strings with Uncertainties}},
  booktitle =	{27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)},
  pages =	{8:1--8:12},
  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/2016/6084},
  URN =		{urn:nbn:de:0030-drops-60842},
  doi =		{10.4230/LIPIcs.CPM.2016.8},
  annote =	{Keywords: string with don’t cares, partial word, indeterminate string, longest common conservative prefix queries, prefix array}
}

Keywords: string with don’t cares, partial word, indeterminate string, longest common conservative prefix queries, prefix array
Collection: 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)
Issue Date: 2016
Date of publication: 27.06.2016


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