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

University of Haifa, Bar-Ilan University

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	American 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

Keywords

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

All Science Journal Classification (ASJC) codes

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].",

keywords = "Algorithms, Repetitions in strings, Straight-line programs, String processing, Text compression",

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.",

year = "2012",

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doi = "10.1016/j.ipl.2012.06.017",

language = "American English",

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T1 - An efficient algorithm to test square-freeness of strings compressed by straight-line programs

AU - Bannai, Hideo

AU - Gagie, Travis

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.

PY - 2012/10/15

Y1 - 2012/10/15

N2 - 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].

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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JO - Information Processing Letters

JF - Information Processing Letters

IS - 19

ER -

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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