Testing square-freeness of strings compressed by balanced straight line program

Wataru Matsubara, Shunsuke Inenaga, Ayumi Shinohara

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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.

Original languageEnglish
Title of host publicationTheory of Computing 2009 - Proceedings of the Fifteenth Computing: The Australasian Theory Symposium, CATS 2009
Volume94
Publication statusPublished - 2009
EventTheory of Computing 2009 - 15th Computing: The Australasian Theory Symposium, CATS 2009 - Wellington, New Zealand
Duration: Jan 20 2009Jan 23 2009

Other

OtherTheory of Computing 2009 - 15th Computing: The Australasian Theory Symposium, CATS 2009
CountryNew Zealand
CityWellington
Period1/20/091/23/09

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Computer Science Applications
  • Hardware and Architecture
  • Information Systems
  • Software

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  • Cite this

    Matsubara, W., Inenaga, S., & Shinohara, A. (2009). Testing square-freeness of strings compressed by balanced straight line program. In Theory of Computing 2009 - Proceedings of the Fifteenth Computing: The Australasian Theory Symposium, CATS 2009 (Vol. 94)