Detecting regularities on grammar-compressed strings

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

doi:10.1016/j.ic.2014.09.009

Detecting regularities on grammar-compressed strings

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

INF - System Information Sciences

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

Abstract

We address the problems of detecting and counting various forms of regularities in a string represented as a straight-line program (SLP) which is essentially a context free grammar in the Chomsky normal form. 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(n3h) 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(n3h+gnhlogN) time and O(n2) space, where g is the length of the gap. As one of the main components of the above solution, we propose a new technique called approximate doubling which seems to be a useful tool for a wide range of algorithms on SLPs. Indeed, we show that the technique can be used to compute the periods and covers of the string in O(n2h) time and O(nh(n+log²N)) time, respectively.

Original language	English
Journal	Information and Computation
DOIs	https://doi.org/10.1016/j.ic.2014.09.009
Publication status	Accepted/In press - 2013 Oct 1

Keywords

Compressed string processing algorithms
Gapped palindromes
Runs
Squares
Straight-line programs (SLPs)

ASJC Scopus subject areas

Information Systems
Computational Theory and Mathematics
Theoretical Computer Science
Computer Science Applications

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10.1016/j.ic.2014.09.009

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title = "Detecting regularities on grammar-compressed strings",

abstract = "We address the problems of detecting and counting various forms of regularities in a string represented as a straight-line program (SLP) which is essentially a context free grammar in the Chomsky normal form. 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(n3h) 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(n3h+gnhlogN) time and O(n2) space, where g is the length of the gap. As one of the main components of the above solution, we propose a new technique called approximate doubling which seems to be a useful tool for a wide range of algorithms on SLPs. Indeed, we show that the technique can be used to compute the periods and covers of the string in O(n2h) time and O(nh(n+log2N)) time, respectively.",

keywords = "Compressed string processing algorithms, Gapped palindromes, Runs, Squares, Straight-line programs (SLPs)",

author = "I. Tomohiro and Wataru Matsubara and Kouji Shimohira and Shunsuke Inenaga and Hideo Bannai and Masayuki Takeda and Kazuyuki Narisawa and Ayumi Shinohara",

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AU - Tomohiro, I.

AU - Matsubara, Wataru

AU - Shimohira, Kouji

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

AU - Narisawa, Kazuyuki

AU - Shinohara, Ayumi

PY - 2013/10/1

Y1 - 2013/10/1

N2 - We address the problems of detecting and counting various forms of regularities in a string represented as a straight-line program (SLP) which is essentially a context free grammar in the Chomsky normal form. 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(n3h) 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(n3h+gnhlogN) time and O(n2) space, where g is the length of the gap. As one of the main components of the above solution, we propose a new technique called approximate doubling which seems to be a useful tool for a wide range of algorithms on SLPs. Indeed, we show that the technique can be used to compute the periods and covers of the string in O(n2h) time and O(nh(n+log2N)) time, respectively.

AB - We address the problems of detecting and counting various forms of regularities in a string represented as a straight-line program (SLP) which is essentially a context free grammar in the Chomsky normal form. 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(n3h) 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(n3h+gnhlogN) time and O(n2) space, where g is the length of the gap. As one of the main components of the above solution, we propose a new technique called approximate doubling which seems to be a useful tool for a wide range of algorithms on SLPs. Indeed, we show that the technique can be used to compute the periods and covers of the string in O(n2h) time and O(nh(n+log2N)) time, respectively.

KW - Compressed string processing algorithms

KW - Gapped palindromes

KW - Runs

KW - Squares

KW - Straight-line programs (SLPs)

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Detecting regularities on grammar-compressed strings

Abstract

Keywords

ASJC Scopus subject areas

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