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
Subtitle of host publicationThe Australasian Theory Symposium, CATS 2009
Publication statusPublished - 2009 Dec 1
EventTheory of Computing 2009 - 15th Computing: The Australasian Theory Symposium, CATS 2009 - Wellington, New Zealand
Duration: 2009 Jan 202009 Jan 23

Publication series

NameConferences in Research and Practice in Information Technology Series
Volume94
ISSN (Print)1445-1336

Other

OtherTheory of Computing 2009 - 15th Computing: The Australasian Theory Symposium, CATS 2009
CountryNew Zealand
CityWellington
Period09/1/2009/1/23

Keywords

  • Balanced straight line program
  • Repetitions
  • Squares
  • String algorithm
  • Text compression

ASJC Scopus subject areas

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

Fingerprint Dive into the research topics of 'Testing square-freeness of strings compressed by balanced straight line program'. Together they form a unique fingerprint.

  • 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 (Conferences in Research and Practice in Information Technology Series; Vol. 94).