### Abstract

The directed acyclic word graph (DAWG) of a string y is the smallest (partial) DFA which recognizes all suffixes of y and has only O(n) nodes and edges. We present the first O(n)-time algorithm for computing the DAWG of a given string y of length n over an integer alphabet of polynomial size in n. We also show that a straightforward modification to our DAWG construction algorithm leads to the first O(n)-time algorithm for constructing the affix tree of a given string y over an integer alphabet. Affix trees are a text indexing structure supporting bidirectional pattern searches. As an application to our O(n)-time DAWG construction algorithm, we show that the set MAW(y) of all minimal absent words of y can be computed in optimal O(n +MAW(y)) time and O(n) working space for integer alphabets.

Original language | English |
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Title of host publication | 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016 |

Editors | Anca Muscholl, Piotr Faliszewski, Rolf Niedermeier |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Electronic) | 9783959770163 |

DOIs | |

Publication status | Published - Aug 1 2016 |

Event | 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016 - Krakow, Poland Duration: Aug 22 2016 → Aug 26 2016 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 58 |

ISSN (Print) | 1868-8969 |

### Other

Other | 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016 |
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Country | Poland |

City | Krakow |

Period | 8/22/16 → 8/26/16 |

### All Science Journal Classification (ASJC) codes

- Software

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## Cite this

*41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016*[38] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 58). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.MFCS.2016.38