### Abstract

A non-linear text is a directed graph where each vertex is labeled with a string. In this paper, we introduce the longest common substring/subsequence problems on non-linear texts. Firstly, we present an algorithm to compute the longest common substring of non-linear texts G _{1} and G _{2} in O(|E _{1}||E _{2}|) time and O(|V _{1}||V _{2}|) space, when at least one of G _{1} and G _{2} is acyclic. Here, V _{i} and E _{i} are the sets of vertices and arcs of input non-linear text G _{i}, respectively, for 1≤i≤2. Secondly, we present algorithms to compute the longest common subsequence of G _{1} and G _{2} in O(|E _{1}||E _{2}|) time and O(|V _{1}||V _{2}|) space, when both G _{1} and G _{2} are acyclic, and in O(|E _{1}||E _{2}|+|V _{1}||V _{2}| log |Σ|) time and O(|V _{1}||V _{2}|) space if G _{1} and/or G _{2} are cyclic, where, Σ denotes the alphabet.

Original language | English |
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Title of host publication | Proceedings of the Prague Stringology Conference 2011 |

Pages | 197-208 |

Number of pages | 12 |

Publication status | Published - 2011 |

Event | Prague Stringology Conference 2011, PSC 2011 - Prague, Czech Republic Duration: Aug 29 2011 → Aug 31 2011 |

### Other

Other | Prague Stringology Conference 2011, PSC 2011 |
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Country | Czech Republic |

City | Prague |

Period | 8/29/11 → 8/31/11 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Proceedings of the Prague Stringology Conference 2011*(pp. 197-208)

**Computing longest common substring/subsequence of non-linear texts.** / Shimohira, Kouji; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki.

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

*Proceedings of the Prague Stringology Conference 2011.*pp. 197-208, Prague Stringology Conference 2011, PSC 2011, Prague, Czech Republic, 8/29/11.

}

TY - GEN

T1 - Computing longest common substring/subsequence of non-linear texts

AU - Shimohira, Kouji

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

PY - 2011

Y1 - 2011

N2 - A non-linear text is a directed graph where each vertex is labeled with a string. In this paper, we introduce the longest common substring/subsequence problems on non-linear texts. Firstly, we present an algorithm to compute the longest common substring of non-linear texts G 1 and G 2 in O(|E 1||E 2|) time and O(|V 1||V 2|) space, when at least one of G 1 and G 2 is acyclic. Here, V i and E i are the sets of vertices and arcs of input non-linear text G i, respectively, for 1≤i≤2. Secondly, we present algorithms to compute the longest common subsequence of G 1 and G 2 in O(|E 1||E 2|) time and O(|V 1||V 2|) space, when both G 1 and G 2 are acyclic, and in O(|E 1||E 2|+|V 1||V 2| log |Σ|) time and O(|V 1||V 2|) space if G 1 and/or G 2 are cyclic, where, Σ denotes the alphabet.

AB - A non-linear text is a directed graph where each vertex is labeled with a string. In this paper, we introduce the longest common substring/subsequence problems on non-linear texts. Firstly, we present an algorithm to compute the longest common substring of non-linear texts G 1 and G 2 in O(|E 1||E 2|) time and O(|V 1||V 2|) space, when at least one of G 1 and G 2 is acyclic. Here, V i and E i are the sets of vertices and arcs of input non-linear text G i, respectively, for 1≤i≤2. Secondly, we present algorithms to compute the longest common subsequence of G 1 and G 2 in O(|E 1||E 2|) time and O(|V 1||V 2|) space, when both G 1 and G 2 are acyclic, and in O(|E 1||E 2|+|V 1||V 2| log |Σ|) time and O(|V 1||V 2|) space if G 1 and/or G 2 are cyclic, where, Σ denotes the alphabet.

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UR - http://www.scopus.com/inward/citedby.url?scp=84869117991&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9788001048702

SP - 197

EP - 208

BT - Proceedings of the Prague Stringology Conference 2011

ER -