### Abstract

This paper studies two problems on compressed strings described in terms of straight line programs (SLPs). One is to compute the length of the longest common substring of two given SLP-compressed strings, and the other is to compute all palindromes of a given SLP-compressed string. In order to solve these problems efficiently (in polynomial time w.r.t. the compressed size) decompression is never feasible, since the decompressed size can be exponentially large. We develop combinatorial algorithms that solve these problems in O (n^{4} log n) time with O (n^{3}) space, and in O (n^{4}) time with O (n^{2}) space, respectively, where n is the size of the input SLP-compressed strings.

Original language | English |
---|---|

Pages (from-to) | 900-913 |

Number of pages | 14 |

Journal | Theoretical Computer Science |

Volume | 410 |

Issue number | 8-10 |

DOIs | |

Publication status | Published - 2009 Mar 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Longest common substring
- Palindromes
- Straight line program
- String processing algorithms
- Text compression

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Theoretical Computer Science*,

*410*(8-10), 900-913. https://doi.org/10.1016/j.tcs.2008.12.016

**Efficient algorithms to compute compressed longest common substrings and compressed palindromes.** / Matsubara, Wataru; Inenaga, Shunsuke; Ishino, Akira; Shinohara, Ayumi; Nakamura, Tomoyuki; Hashimoto, Kazuo.

Research output: Contribution to journal › Article

*Theoretical Computer Science*, vol. 410, no. 8-10, pp. 900-913. https://doi.org/10.1016/j.tcs.2008.12.016

}

TY - JOUR

T1 - Efficient algorithms to compute compressed longest common substrings and compressed palindromes

AU - Matsubara, Wataru

AU - Inenaga, Shunsuke

AU - Ishino, Akira

AU - Shinohara, Ayumi

AU - Nakamura, Tomoyuki

AU - Hashimoto, Kazuo

PY - 2009/3/1

Y1 - 2009/3/1

N2 - This paper studies two problems on compressed strings described in terms of straight line programs (SLPs). One is to compute the length of the longest common substring of two given SLP-compressed strings, and the other is to compute all palindromes of a given SLP-compressed string. In order to solve these problems efficiently (in polynomial time w.r.t. the compressed size) decompression is never feasible, since the decompressed size can be exponentially large. We develop combinatorial algorithms that solve these problems in O (n4 log n) time with O (n3) space, and in O (n4) time with O (n2) space, respectively, where n is the size of the input SLP-compressed strings.

AB - This paper studies two problems on compressed strings described in terms of straight line programs (SLPs). One is to compute the length of the longest common substring of two given SLP-compressed strings, and the other is to compute all palindromes of a given SLP-compressed string. In order to solve these problems efficiently (in polynomial time w.r.t. the compressed size) decompression is never feasible, since the decompressed size can be exponentially large. We develop combinatorial algorithms that solve these problems in O (n4 log n) time with O (n3) space, and in O (n4) time with O (n2) space, respectively, where n is the size of the input SLP-compressed strings.

KW - Longest common substring

KW - Palindromes

KW - Straight line program

KW - String processing algorithms

KW - Text compression

UR - http://www.scopus.com/inward/record.url?scp=59049103692&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=59049103692&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2008.12.016

DO - 10.1016/j.tcs.2008.12.016

M3 - Article

VL - 410

SP - 900

EP - 913

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 8-10

ER -