### Abstract

The directed acyclic word graph (DAWG) of a string y is the smallest (partial) DFA which recognizes all suffixes of y and has O(n) nodes and edges. Na et al. [11] proposed k-truncated suffix tree which is a compressed trie that represents substrings of a string whose length up to k. In this paper, we present a new data structure called k-truncated DAWGs, which can be obtained by pruning the DAWGs. We show that the size complexity of the k-truncated DAWG of a string y of length n is O(min{{n,kz}) which is equal to the truncated suffix tree’s one, where z is the size of LZ77 factorization of y. We also present an O(n log σ) time and O(min{{n,kz}) space algorithm for constructing the k-truncated DAWG of y, where σ is the alphabet size. As an application of the truncated DAWGs, we show that the set MAW_{k}(y) of all minimal absent words of y whose length is smaller than or equal to k can be computed by using k-truncated DAWG of y in O(min{{n,kz}) + |MAW_{k}(y)|) time and O(min{{n,kz}) working space.

Original language | English |
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Title of host publication | String Processing and Information Retrieval - 25th International Symposium, SPIRE 2018, Proceedings |

Editors | Travis Gagie, Alistair Moffat, Gonzalo Navarro, Ernesto Cuadros-Vargas |

Publisher | Springer Verlag |

Pages | 139-152 |

Number of pages | 14 |

ISBN (Print) | 9783030004781 |

DOIs | |

Publication status | Published - 2018 Jan 1 |

Event | 25th International Symposium on String Processing and Information Retrieval, SPIRE 2018 - Lima, Peru Duration: 2018 Oct 9 → 2018 Oct 11 |

### 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 | 11147 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 25th International Symposium on String Processing and Information Retrieval, SPIRE 2018 |
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Country | Peru |

City | Lima |

Period | 18/10/9 → 18/10/11 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*String Processing and Information Retrieval - 25th International Symposium, SPIRE 2018, Proceedings*(pp. 139-152). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11147 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-00479-8_12