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.MFCS.2016.69
URN: urn:nbn:de:0030-drops-65033
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6503/
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Mieno, Takuya ; Inenaga, Shunsuke ; Bannai, Hideo ; Takeda, Masayuki

Shortest Unique Substring Queries on Run-Length Encoded Strings

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LIPIcs-MFCS-2016-69.pdf (0.7 MB)

Abstract

We consider the problem of answering shortest unique substring (SUS) queries on run-length encoded strings. For a string S, a unique substring u = S[i..j] is said to be a shortest unique substring (SUS) of S containing an interval [s, t] (i <= s <= t <= j) if for any i' <= s <= t <= j' with j-i > j'-i', S[i'..j'] occurs at least twice in S.
Given a run-length encoding of size m of a string of length N, we show that we can construct a data structure of size O(m+pi_s(N, m)) in O(m log m + pi_c(N, m)) time such that queries can be answered in
O(pi_q(N, m) + k) time, where k is the size of the output (the number of SUSs), and pi_s(N,m), pi_c(N,m), pi_q(N,m) are, respectively, the size, construction time, and query time for a predecessor/successor query data structure of m elements for the universe of [1,N]. Using the data structure by Beam and Fich (JCSS 2002), this results in a data structure of O(m) space that is constructed in O(m log m) time, and answers queries in O(sqrt(log m/loglog m)+k) time.

BibTeX - Entry

@InProceedings{mieno_et_al:LIPIcs:2016:6503,
  author =	{Takuya Mieno and Shunsuke Inenaga and Hideo Bannai and Masayuki Takeda},
  title =	{{Shortest Unique Substring Queries on Run-Length Encoded Strings}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{69:1--69:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Piotr Faliszewski and Anca Muscholl and Rolf Niedermeier},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6503},
  URN =		{urn:nbn:de:0030-drops-65033},
  doi =		{10.4230/LIPIcs.MFCS.2016.69},
  annote =	{Keywords: string algorithms, shortest unique substring, run-length encoding}
}

Keywords: string algorithms, shortest unique substring, run-length encoding
Collection: 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)
Issue Date: 2016
Date of publication: 19.08.2016

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