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DOI: 10.4230/LIPIcs.CPM.2016.27
URN: urn:nbn:de:0030-drops-60645
URL: https://drops.dagstuhl.de/opus/volltexte/2016/6064/
Matsuoka, Yoshiaki ; Inenaga, Shunsuke ; Bannai, Hideo ; Takeda, Masayuki ; Manea, Florin
Factorizing a String into Squares in Linear Time
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Abstract
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
@InProceedings{matsuoka_et_al:LIPIcs:2016:6064,
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 = {http://drops.dagstuhl.de/opus/volltexte/2016/6064},
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 | |
| Seminar: | 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016) | |
| Issue date: | 2016 | |
| Date of publication: | 27.06.2016 |
