### Abstract

A substring u of a string T is called a minimal unique substring (MUS) of T if u occurs exactly once in T and any proper substring of u occurs at least twice in T. A string w is called a minimal absent word (MAW) of T if w does not occur in T and any proper substring of w occurs in T. In this paper, we study the problems of computing MUSs and MAWs in a sliding window over a given string T. We first show how the set of MUSs can change in a sliding window over T, and present an-time and O(d)-space algorithm to compute MUSs in a sliding window of width d over T, where is the maximum number of distinct characters in every window. We then give tight upper and lower bounds on the maximum number of changes in the set of MAWs in a sliding window over T. Our bounds improve on the previous results in Crochemore et al. (2017).

Original language | English |
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Title of host publication | SOFSEM 2020 |

Subtitle of host publication | Theory and Practice of Computer Science - 46th International Conference on Current Trends in Theory and Practice of Informatics, SOFSEM 2020, Proceedings |

Editors | Alexander Chatzigeorgiou, Riccardo Dondi, Herodotos Herodotou, Christos Kapoutsis, Yannis Manolopoulos, George A. Papadopoulos, Florian Sikora |

Publisher | Springer |

Pages | 148-160 |

Number of pages | 13 |

ISBN (Print) | 9783030389185 |

DOIs | |

Publication status | Published - Jan 1 2020 |

Event | 46th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2020 - Limassol, Cyprus Duration: Jan 20 2020 → Jan 24 2020 |

### 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 | 12011 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 46th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2020 |
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Country | Cyprus |

City | Limassol |

Period | 1/20/20 → 1/24/20 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*SOFSEM 2020: Theory and Practice of Computer Science - 46th International Conference on Current Trends in Theory and Practice of Informatics, SOFSEM 2020, Proceedings*(pp. 148-160). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12011 LNCS). Springer. https://doi.org/10.1007/978-3-030-38919-2_13