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

Authors: Wataru Matsubara, Shunsuke Inenaga, and Ayumi Shinohara

Published in: Dagstuhl Seminar Proceedings, Volume 8261, Structure-Based Compression of Complex Massive Data (2008)

Abstract

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.

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Wataru Matsubara, Shunsuke Inenaga, and Ayumi Shinohara. An Efficient Algorithm to Test Square-Freeness of Strings Compressed by Balanced Straight Line Program. In Structure-Based Compression of Complex Massive Data. Dagstuhl Seminar Proceedings, Volume 8261, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{matsubara_et_al:DagSemProc.08261.5,
  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 =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08261.5},
  URN =		{urn:nbn:de:0030-drops-16804},
  doi =		{10.4230/DagSemProc.08261.5},
  annote =	{Keywords: Square Freeness, Straight Line Program}
}

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

Abstract

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