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.2018.15
URN: urn:nbn:de:0030-drops-86946
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Inoue, Takafumi ; Inenaga, Shunsuke ; Hyyrö, Heikki ; Bannai, Hideo ; Takeda, Masayuki

Computing longest common square subsequences

LIPIcs-CPM-2018-15.pdf (0.6 MB)


A square is a non-empty string of form YY. The longest common square subsequence (LCSqS) problem is to compute a longest square occurring as a subsequence in two given strings A and B. We show that the problem can easily be solved in O(n^6) time or O(|M|n^4) time with O(n^4) space, where n is the length of the strings and M is the set of matching points between A and B. Then, we show that the problem can also be solved in O(sigma |M|^3 + n) time and O(|M|^2 + n) space, or in O(|M|^3 log^2 n log log n + n) time with O(|M|^3 + n) space, where sigma is the number of distinct characters occurring in A and B. We also study lower bounds for the LCSqS problem for two or more strings.

BibTeX - Entry

  author =	{Takafumi Inoue and Shunsuke Inenaga and Heikki Hyyr{\"o} and Hideo Bannai and Masayuki Takeda},
  title =	{{Computing longest common square subsequences}},
  booktitle =	{Annual Symposium on Combinatorial Pattern Matching  (CPM 2018)},
  pages =	{15:1--15:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-074-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{105},
  editor =	{Gonzalo Navarro and David Sankoff and Binhai Zhu},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-86946},
  doi =		{10.4230/LIPIcs.CPM.2018.15},
  annote =	{Keywords: squares, subsequences, matching rectangles, dynamic programming}

Keywords: squares, subsequences, matching rectangles, dynamic programming
Collection: Annual Symposium on Combinatorial Pattern Matching (CPM 2018)
Issue Date: 2018
Date of publication: 18.05.2018

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