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.ISAAC.2017.35
URN: urn:nbn:de:0030-drops-82566
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8256/
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Ganguly, Arnab ; Shah, Rahul ; Thankachan, Sharma V.

Structural Pattern Matching - Succinctly

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LIPIcs-ISAAC-2017-35.pdf (0.6 MB)

Abstract

Let T be a text of length n containing characters from an alphabet \Sigma, which is the union of two disjoint sets: \Sigma_s containing static characters (s-characters) and \Sigma_p containing parameterized characters (p-characters).
Each character in \Sigma_p has an associated complementary character from \Sigma_p.
A pattern P (also over \Sigma) matches an equal-length substring $S$ of T iff the s-characters match exactly, there exists a one-to-one function that renames the p-characters in S to the p-characters in P, and if a p-character x is renamed to another p-character y then the complement of x is renamed to the complement of y.
The task is to find the starting positions (occurrences) of all such substrings S.
Previous indexing solution [Shibuya, SWAT 2000], known as Structural Suffix Tree, requires \Theta(n\log n) bits of space, and can find all occ occurrences in time O(|P|\log \sigma+ occ), where \sigma = |\Sigma|.
In this paper, we present the first succinct index for this problem, which occupies n \log \sigma + O(n) bits and offers O(|P|\log\sigma+ occ\cdot \log n \log\sigma) query time.

BibTeX - Entry

@InProceedings{ganguly_et_al:LIPIcs:2017:8256,
  author =	{Arnab Ganguly and Rahul Shah and Sharma V. Thankachan},
  title =	{{Structural Pattern Matching - Succinctly}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{35:1--35:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Yoshio Okamoto and Takeshi Tokuyama},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8256},
  URN =		{urn:nbn:de:0030-drops-82566},
  doi =		{10.4230/LIPIcs.ISAAC.2017.35},
  annote =	{Keywords: Parameterized Pattern Matching, Suffix tree, Burrows-Wheeler Transform, Wavelet Tree, Fully-functional succinct tree}
}

Keywords: Parameterized Pattern Matching, Suffix tree, Burrows-Wheeler Transform, Wavelet Tree, Fully-functional succinct tree
Collection: 28th International Symposium on Algorithms and Computation (ISAAC 2017)
Issue Date: 2017
Date of publication: 07.12.2017

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