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.2019.15
URN: urn:nbn:de:0030-drops-104865
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10486/
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Studený, Jan ; Uznanski, Przemyslaw

Approximating Approximate Pattern Matching

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LIPIcs-CPM-2019-15.pdf (0.5 MB)


Abstract

Given a text T of length n and a pattern P of length m, the approximate pattern matching problem asks for computation of a particular distance function between P and every m-substring of T. We consider a (1 +/- epsilon) multiplicative approximation variant of this problem, for l_p distance function. In this paper, we describe two (1+epsilon)-approximate algorithms with a runtime of O~(n/epsilon) for all (constant) non-negative values of p. For constant p >= 1 we show a deterministic (1+epsilon)-approximation algorithm. Previously, such run time was known only for the case of l_1 distance, by Gawrychowski and Uznanski [ICALP 2018] and only with a randomized algorithm. For constant 0 <= p <= 1 we show a randomized algorithm for the l_p, thereby providing a smooth tradeoff between algorithms of Kopelowitz and Porat [FOCS 2015, SOSA 2018] for Hamming distance (case of p=0) and of Gawrychowski and Uznanski for l_1 distance.

BibTeX - Entry

@InProceedings{studen_et_al:LIPIcs:2019:10486,
  author =	{Jan Studen{\'y} and Przemyslaw Uznanski},
  title =	{{Approximating Approximate Pattern Matching}},
  booktitle =	{30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)},
  pages =	{15:1--15:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-103-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{128},
  editor =	{Nadia Pisanti and Solon P. Pissis},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10486},
  URN =		{urn:nbn:de:0030-drops-104865},
  doi =		{10.4230/LIPIcs.CPM.2019.15},
  annote =	{Keywords: Approximate Pattern Matching, l_p Distance, l_1 Distance, Hamming Distance, Approximation Algorithms}
}

Keywords: Approximate Pattern Matching, l_p Distance, l_1 Distance, Hamming Distance, Approximation Algorithms
Collection: 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)
Issue Date: 2019
Date of publication: 06.06.2019


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