An efficient algorithm to test square-freeness of strings compressed by straight-line programs

Hideo Bannai; Travis Gagie; Tomohiro I; Shunsuke Inenaga; Gad M. Landau; Moshe Lewenstein

doi:10.1016/j.ipl.2012.06.017

An efficient algorithm to test square-freeness of strings compressed by straight-line programs

Hideo Bannai
, Travis Gagie
, Tomohiro I
, Shunsuke Inenaga
, Gad M. Landau
, Moshe Lewenstein

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

We give a simple algorithm that, given a straight-line program of size n for a string S of length N, tests whether S is square-free in O(n ⁴logN) time and O(n²) space. The algorithm also allows us to test square-freeness on an arbitrary composition system of size c for S, in O(c⁴log⁵N) time and O(c²log²N) space, which is faster than using the algorithm by Ga̧sieniec, Karpinski, Plandowski, and Rytter (1996) [4].

Original language	English
Pages (from-to)	711-714
Number of pages	4
Journal	Information Processing Letters
Volume	112
Issue number	19
DOIs	https://doi.org/10.1016/j.ipl.2012.06.017
State	Published - 15 Oct 2012

Bibliographical note

Funding Information:
1Partially supported by the National Science Foundation Award 0904246, Israel Science Foundation grant 347/09, Grant No. 2008217 from the United States–Israel Binational Science Foundation (BSF) and DFG.

Keywords

Algorithms
Repetitions in strings
Straight-line programs
String processing
Text compression

ASJC Scopus subject areas

Theoretical Computer Science
Signal Processing
Information Systems
Computer Science Applications

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10.1016/j.ipl.2012.06.017

Cite this

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title = "An efficient algorithm to test square-freeness of strings compressed by straight-line programs",

abstract = "We give a simple algorithm that, given a straight-line program of size n for a string S of length N, tests whether S is square-free in O(n 4logN) time and O(n2) space. The algorithm also allows us to test square-freeness on an arbitrary composition system of size c for S, in O(c4log5N) time and O(c2log2N) space, which is faster than using the algorithm by G{\c a}sieniec, Karpinski, Plandowski, and Rytter (1996) [4].",

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author = "Hideo Bannai and Travis Gagie and Tomohiro I and Shunsuke Inenaga and Landau, \{Gad M.\} and Moshe Lewenstein",

note = "Funding Information: 1Partially supported by the National Science Foundation Award 0904246, Israel Science Foundation grant 347/09, Grant No. 2008217 from the United States–Israel Binational Science Foundation (BSF) and DFG.",

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AU - I, Tomohiro

AU - Inenaga, Shunsuke

AU - Landau, Gad M.

AU - Lewenstein, Moshe

N1 - Funding Information: 1Partially supported by the National Science Foundation Award 0904246, Israel Science Foundation grant 347/09, Grant No. 2008217 from the United States–Israel Binational Science Foundation (BSF) and DFG.

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AB - We give a simple algorithm that, given a straight-line program of size n for a string S of length N, tests whether S is square-free in O(n 4logN) time and O(n2) space. The algorithm also allows us to test square-freeness on an arbitrary composition system of size c for S, in O(c4log5N) time and O(c2log2N) space, which is faster than using the algorithm by Ga̧sieniec, Karpinski, Plandowski, and Rytter (1996) [4].

KW - Algorithms

KW - Repetitions in strings

KW - Straight-line programs

KW - String processing

KW - Text compression

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An efficient algorithm to test square-freeness of strings compressed by straight-line programs

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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