### Abstract

We consider the problem of answering shortest unique substring (SUS) queries on run-length encoded strings. For a string S, a unique substring u = S[i..j] is said to be a shortest unique substring (SUS) of S containing an interval [s, t] (i ≤ s ≤ t ≤ j) if for any i0 ≤ s ≤t ≤j0 with j - i > j0 - i0, S[i0..j0] occurs at least twice in S. Given a run-length encoding of size m of a string of length N, we show that we can construct a data structure of size O(m + πs(N,m)) in O(mlogm + πc(N,m)) time such that queries can be answered in O(πq(N,m) + k) time, where k is the size of the output (the number of SUSs), and πs(N,m), πc(N,m), πq(N,m) are, respectively, the size, construction time, and query time for a predecessor/successor query data structure of m elements for the universe of [1,N]. Using the data structure by Beam and Fich (JCSS 2002), this results in a data structure of O(m) space that is constructed in O(mlogm) time, and answers queries in O( √ log m/log logm + k) time.

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*[69] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 58). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.MFCS.2016.69