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.2019.40
URN: urn:nbn:de:0030-drops-115366
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11536/
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Fujishige, Yuta ; Nakashima, Yuto ; Inenaga, Shunsuke ; Bannai, Hideo ; Takeda, Masayuki

An Improved Data Structure for Left-Right Maximal Generic Words Problem

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LIPIcs-ISAAC-2019-40.pdf (0.7 MB)

Abstract

For a set D of documents and a positive integer d, a string w is said to be d-left-right maximal, if (1) w occurs in at least d documents in D, and (2) any proper superstring of w occurs in less than d documents. The left-right-maximal generic words problem is, given a set D of documents, to preprocess D so that for any string p and for any positive integer d, all the superstrings of p that are d-left-right maximal can be answered quickly. In this paper, we present an O(n log m) space data structure (in words) which answers queries in O(|p| + o log log m) time, where n is the total length of documents in D, m is the number of documents in D and o is the number of outputs. Our solution improves the previous one by Nishimoto et al. (PSC 2015), which uses an O(n log n) space data structure answering queries in O(|p|+ r * log n + o * log^2 n) time, where r is the number of right-extensions q of p occurring in at least d documents such that any proper right extension of q occurs in less than d documents.

BibTeX - Entry

@InProceedings{fujishige_et_al:LIPIcs:2019:11536,
  author =	{Yuta Fujishige and Yuto Nakashima and Shunsuke Inenaga and Hideo Bannai and Masayuki Takeda},
  title =	{{An Improved Data Structure for Left-Right Maximal Generic Words Problem}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{40:1--40:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Pinyan Lu and Guochuan Zhang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11536},
  URN =		{urn:nbn:de:0030-drops-115366},
  doi =		{10.4230/LIPIcs.ISAAC.2019.40},
  annote =	{Keywords: generic words, suffix trees, string processing algorithms}
}

Keywords: generic words, suffix trees, string processing algorithms
Collection: 30th International Symposium on Algorithms and Computation (ISAAC 2019)
Issue Date: 2019
Date of publication: 28.11.2019

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