### Abstract

Given a set S of strings, a DFA accepting S offers a very time-efficient solution to the pattern matching problem over S. The key is how to implement such a DFA in the trade-off between time and space, and especially the choice of how to implement the transitions of each state is critical. Bentley and Sedgewick proposed an effective tree structure called ternary trees. The idea of ternary trees is to ‘implant’ the process of binary search for transitions into the structure of the trees themselves. This way the process of binary search becomes visible, and the implementation of the trees becomes quite easy. The directed acyclic word graph (DAWG) of a string w is the smallest DFA that accepts all suffixes of w, and requires only linear space. We apply the scheme of ternary trees to DAWGs, introducing a new data structure named ternary DAWGs (TDAWGs). We perform some experiments that show the efficiency of TDAWGs, compared to DAWGs in which transitions are implemented by tables and linked lists.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Editors | Oscar H. Ibarra, Zhe Dang |

Publisher | Springer Verlag |

Pages | 108-120 |

Number of pages | 13 |

ISBN (Print) | 3540405615 |

Publication status | Published - Jan 1 2003 |

Event | 8th International Conference on Implementation and Application of Automata, CIAA 2003 - Santa Barbara, United States Duration: Jul 16 2003 → Jul 18 2003 |

### 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 | 2759 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 8th International Conference on Implementation and Application of Automata, CIAA 2003 |
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Country | United States |

City | Santa Barbara |

Period | 7/16/03 → 7/18/03 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(pp. 108-120). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2759). Springer Verlag.

**Ternary directed acyclic word graphs.** / Miyamoto, Satoru; Inenaga, Shunsuke; Takeda, Masayuki; Shinohara, Ayumi.

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

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2759, Springer Verlag, pp. 108-120, 8th International Conference on Implementation and Application of Automata, CIAA 2003, Santa Barbara, United States, 7/16/03.

}

TY - GEN

T1 - Ternary directed acyclic word graphs

AU - Miyamoto, Satoru

AU - Inenaga, Shunsuke

AU - Takeda, Masayuki

AU - Shinohara, Ayumi

PY - 2003/1/1

Y1 - 2003/1/1

N2 - Given a set S of strings, a DFA accepting S offers a very time-efficient solution to the pattern matching problem over S. The key is how to implement such a DFA in the trade-off between time and space, and especially the choice of how to implement the transitions of each state is critical. Bentley and Sedgewick proposed an effective tree structure called ternary trees. The idea of ternary trees is to ‘implant’ the process of binary search for transitions into the structure of the trees themselves. This way the process of binary search becomes visible, and the implementation of the trees becomes quite easy. The directed acyclic word graph (DAWG) of a string w is the smallest DFA that accepts all suffixes of w, and requires only linear space. We apply the scheme of ternary trees to DAWGs, introducing a new data structure named ternary DAWGs (TDAWGs). We perform some experiments that show the efficiency of TDAWGs, compared to DAWGs in which transitions are implemented by tables and linked lists.

AB - Given a set S of strings, a DFA accepting S offers a very time-efficient solution to the pattern matching problem over S. The key is how to implement such a DFA in the trade-off between time and space, and especially the choice of how to implement the transitions of each state is critical. Bentley and Sedgewick proposed an effective tree structure called ternary trees. The idea of ternary trees is to ‘implant’ the process of binary search for transitions into the structure of the trees themselves. This way the process of binary search becomes visible, and the implementation of the trees becomes quite easy. The directed acyclic word graph (DAWG) of a string w is the smallest DFA that accepts all suffixes of w, and requires only linear space. We apply the scheme of ternary trees to DAWGs, introducing a new data structure named ternary DAWGs (TDAWGs). We perform some experiments that show the efficiency of TDAWGs, compared to DAWGs in which transitions are implemented by tables and linked lists.

UR - http://www.scopus.com/inward/record.url?scp=84944328633&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84944328633&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84944328633

SN - 3540405615

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

SP - 108

EP - 120

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

A2 - Ibarra, Oscar H.

A2 - Dang, Zhe

PB - Springer Verlag

ER -