License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.08261.5
URN: urn:nbn:de:0030-drops-16804
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Matsubara, Wataru ; Inenaga, Shunsuke ; Shinohara, Ayumi

An Efficient Algorithm to Test Square-Freeness of Strings Compressed by Balanced Straight Line Program

08261.MatsubaraWataru.Paper.1680.pdf (0.3 MB)


In this paper we study the problem of deciding whether a
given compressed string contains a square. A string x is called a square
if x = zz and z = u^k implies k = 1 and u = z. A string w is said to be
square-free if no substrings of w are squares. Many efficient algorithms
to test if a given string is square-free, have been developed so far. However,
very little is known for testing square-freeness of a given compressed
string. In this paper, we give an O(max(n^2; n log^2 N))-time O(n^2)-space
solution to test square-freeness of a given compressed string, where n
and N are the size of a given compressed string and the corresponding
decompressed string, respectively. Our input strings are compressed by
balanced straight line program (BSLP). We remark that BSLP has exponential
compression, that is, N = O(2^n). Hence no decompress-then-test
approaches can be better than our method in the worst case.

BibTeX - Entry

  author =	{Matsubara, Wataru and Inenaga, Shunsuke and Shinohara, Ayumi},
  title =	{{An Efficient Algorithm to Test Square-Freeness of Strings Compressed by Balanced Straight Line Program}},
  booktitle =	{Structure-Based Compression of Complex Massive Data},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8261},
  editor =	{Stefan B\"{o}ttcher and Markus Lohrey and Sebastian Maneth and Wojcieh Rytter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-16804},
  doi =		{10.4230/DagSemProc.08261.5},
  annote =	{Keywords: Square Freeness, Straight Line Program}

Keywords: Square Freeness, Straight Line Program
Collection: 08261 - Structure-Based Compression of Complex Massive Data
Issue Date: 2008
Date of publication: 20.11.2008

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