Detecting regularities on grammar-compressed strings

Tomohiro I; Wataru Matsubara; Kouji Shimohira; Shunsuke Inenaga; Hideo Bannai; Masayuki Takeda; Kazuyuki Narisawa; Ayumi Shinohara

doi:10.1007/978-3-642-40313-2_51

Detecting regularities on grammar-compressed strings

Tomohiro I, Wataru Matsubara, Kouji Shimohira, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda, Kazuyuki Narisawa, Ayumi Shinohara

Mathematical Informatics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Citations (Scopus)

Abstract

We solve the problems of detecting and counting various forms of regularities in a string represented as a Straight Line Program (SLP). Given an SLP of size n that represents a string s of length N, our algorithm computes all runs and squares in s in O(n³ h) time and O(n²) space, where h is the height of the derivation tree of the SLP. We also show an algorithm to compute all gapped-palindromes in O(n³ h + gnhlog N) time and O(n²) space, where g is the length of the gap. The key technique of the above solution also allows us to compute the periods and covers of the string in O(n² h) time and O(nh(n + log² N)) time, respectively.

Original language	English
Title of host publication	Mathematical Foundations of Computer Science 2013 - 38th International Symposium, MFCS 2013, Proceedings
Publisher	Springer Verlag
Pages	571-582
Number of pages	12
ISBN (Print)	9783642403125
DOIs	https://doi.org/10.1007/978-3-642-40313-2_51
Publication status	Published - 2013
Event	38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013 - Klosterneuburg, Austria Duration: Aug 26 2013 → Aug 30 2013

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8087
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013
Country/Territory	Austria
City	Klosterneuburg
Period	8/26/13 → 8/30/13

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-642-40313-2_51

Cite this

I, T., Matsubara, W., Shimohira, K., Inenaga, S., Bannai, H., Takeda, M., Narisawa, K., & Shinohara, A. (2013). Detecting regularities on grammar-compressed strings. In Mathematical Foundations of Computer Science 2013 - 38th International Symposium, MFCS 2013, Proceedings (pp. 571-582). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8087). Springer Verlag. https://doi.org/10.1007/978-3-642-40313-2_51

Detecting regularities on grammar-compressed strings. / I, Tomohiro; Matsubara, Wataru; Shimohira, Kouji et al.
Mathematical Foundations of Computer Science 2013 - 38th International Symposium, MFCS 2013, Proceedings. Springer Verlag, 2013. p. 571-582 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8087).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

I, T, Matsubara, W, Shimohira, K, Inenaga, S, Bannai, H, Takeda, M, Narisawa, K & Shinohara, A 2013, Detecting regularities on grammar-compressed strings. in Mathematical Foundations of Computer Science 2013 - 38th International Symposium, MFCS 2013, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8087, Springer Verlag, pp. 571-582, 38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013, Klosterneuburg, Austria, 8/26/13. https://doi.org/10.1007/978-3-642-40313-2_51

I T, Matsubara W, Shimohira K, Inenaga S, Bannai H, Takeda M et al. Detecting regularities on grammar-compressed strings. In Mathematical Foundations of Computer Science 2013 - 38th International Symposium, MFCS 2013, Proceedings. Springer Verlag. 2013. p. 571-582. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-40313-2_51

I, Tomohiro ; Matsubara, Wataru ; Shimohira, Kouji et al. / Detecting regularities on grammar-compressed strings. Mathematical Foundations of Computer Science 2013 - 38th International Symposium, MFCS 2013, Proceedings. Springer Verlag, 2013. pp. 571-582 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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AU - Takeda, Masayuki

AU - Narisawa, Kazuyuki

AU - Shinohara, Ayumi

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N2 - We solve the problems of detecting and counting various forms of regularities in a string represented as a Straight Line Program (SLP). Given an SLP of size n that represents a string s of length N, our algorithm computes all runs and squares in s in O(n3 h) time and O(n2) space, where h is the height of the derivation tree of the SLP. We also show an algorithm to compute all gapped-palindromes in O(n3 h + gnhlog N) time and O(n2) space, where g is the length of the gap. The key technique of the above solution also allows us to compute the periods and covers of the string in O(n2 h) time and O(nh(n + log2 N)) time, respectively.

AB - We solve the problems of detecting and counting various forms of regularities in a string represented as a Straight Line Program (SLP). Given an SLP of size n that represents a string s of length N, our algorithm computes all runs and squares in s in O(n3 h) time and O(n2) space, where h is the height of the derivation tree of the SLP. We also show an algorithm to compute all gapped-palindromes in O(n3 h + gnhlog N) time and O(n2) space, where g is the length of the gap. The key technique of the above solution also allows us to compute the periods and covers of the string in O(n2 h) time and O(nh(n + log2 N)) time, respectively.

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Detecting regularities on grammar-compressed strings

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