### 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(n3) 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 |
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Title of host publication | SOFSEM 2008: Theory and Practice of Computer Science - 34th Conference on Current Trends in Theory and Practice of Computer Science, Proceedings |

Pages | 364-375 |

Number of pages | 12 |

Volume | 4910 LNCS |

Publication status | Published - 2008 |

Event | SOFSEM 2008 - 34th Conference on Current Trends in Theory and Practice of Computer Science - Novy Smokovec, Slovakia Duration: Jan 19 2008 → Jan 25 2008 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4910 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | SOFSEM 2008 - 34th Conference on Current Trends in Theory and Practice of Computer Science |
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Country | Slovakia |

City | Novy Smokovec |

Period | 1/19/08 → 1/25/08 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### Cite this

*SOFSEM 2008: Theory and Practice of Computer Science - 34th Conference on Current Trends in Theory and Practice of Computer Science, Proceedings*(Vol. 4910 LNCS, pp. 364-375). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4910 LNCS).

**Computing longest common substring and all palindromes from compressed strings.** / Matsubara, Wataru; Inenaga, Shunsuke; Ishino, Akira; Shinohara, Ayumi; Nakamura, Tomoyuki; Hashimoto, Kazuo.

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

*SOFSEM 2008: Theory and Practice of Computer Science - 34th Conference on Current Trends in Theory and Practice of Computer Science, Proceedings.*vol. 4910 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4910 LNCS, pp. 364-375, SOFSEM 2008 - 34th Conference on Current Trends in Theory and Practice of Computer Science, Novy Smokovec, Slovakia, 1/19/08.

}

TY - GEN

T1 - Computing longest common substring and all palindromes from compressed strings

AU - Matsubara, Wataru

AU - Inenaga, Shunsuke

AU - Ishino, Akira

AU - Shinohara, Ayumi

AU - Nakamura, Tomoyuki

AU - Hashimoto, Kazuo

PY - 2008

Y1 - 2008

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(n 4) 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(n 4) time with O(n2) space, respectively, where n is the size of the input SLP-compressed strings.

UR - http://www.scopus.com/inward/record.url?scp=38549098620&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38549098620&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:38549098620

SN - 354077565X

SN - 9783540775652

VL - 4910 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 364

EP - 375

BT - SOFSEM 2008: Theory and Practice of Computer Science - 34th Conference on Current Trends in Theory and Practice of Computer Science, Proceedings

ER -