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.2016.27
URN: urn:nbn:de:0030-drops-60645
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Matsuoka, Yoshiaki ; Inenaga, Shunsuke ; Bannai, Hideo ; Takeda, Masayuki ; Manea, Florin

Factorizing a String into Squares in Linear Time

LIPIcs-CPM-2016-27.pdf (0.4 MB)


A square factorization of a string w is a factorization of w in which each factor is a square. Dumitran et al. [SPIRE 2015, pp. 54-66] showed how to find a square factorization of a given string of length n in O(n log n) time, and they posed a question whether it can be done in O(n) time. In this paper, we answer their question positively, showing an O(n)-time algorithm for square factorization in the standard word RAM model with machine word size omega = Omega(log n). We also show an O(n + (n log^2 n) / omega)-time (respectively, O(n log n)-time) algorithm to find a square factorization which contains the maximum (respectively, minimum) number of squares.

BibTeX - Entry

  author =	{Yoshiaki Matsuoka and Shunsuke Inenaga and Hideo Bannai and Masayuki Takeda and Florin Manea},
  title =	{{Factorizing a String into Squares in Linear Time}},
  booktitle =	{27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)},
  pages =	{27:1--27:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-012-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{54},
  editor =	{Roberto Grossi and Moshe Lewenstein},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-60645},
  doi =		{10.4230/LIPIcs.CPM.2016.27},
  annote =	{Keywords: Squares, Runs, Factorization of Strings}

Keywords: Squares, Runs, Factorization of Strings
Collection: 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)
Issue Date: 2016
Date of publication: 27.06.2016

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