## Abstract

In the snippets problem we are interested in preprocessing a text T so that given two pattern queries P_{1} and P_{2}, one can quickly locate the occurrences of the patterns in T that are the closest to each other. A closely related problem is that of constructing a color-distance oracle, where the goal is to preprocess a set of points from some metric space, in which every point is associated with a set of colors, so that given two colors one can quickly locate two points associated with those colors, that are as close as possible to each other. We introduce efficient data structures for both color-distance oracles and the snippets problem. Moreover, we prove conditional lower bounds for these problems from both the 3SUM conjecture and the Combinatorial Boolean Matrix Multiplication conjecture.

Original language | English |
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Title of host publication | 27th Annual Symposium on Combinatorial Pattern Matching, CPM 2016 |

Editors | Roberto Grossi, Moshe Lewenstein |

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

Pages | 24.1-24.10 |

ISBN (Electronic) | 9783959770125 |

DOIs | |

State | Published - 1 Jun 2016 |

Externally published | Yes |

Event | 27th Annual Symposium on Combinatorial Pattern Matching, CPM 2016 - Tel Aviv, Israel Duration: 27 Jun 2016 → 29 Jun 2016 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 54 |

ISSN (Print) | 1868-8969 |

### Conference

Conference | 27th Annual Symposium on Combinatorial Pattern Matching, CPM 2016 |
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Country/Territory | Israel |

City | Tel Aviv |

Period | 27/06/16 → 29/06/16 |

### Bibliographical note

Publisher Copyright:© Tsvi Kopelowitz Robert Krauthgamer.

### Funding

Work supported in part by NSF grants CCF-1217338, CNS-1318294, and CCF-1514383. Work supported in part by an Israel Science Foundation grant #897/13. We thank Sharma Thankachan for suggesting to consider range predecessor data structures, thereby significantly simplifying our earlier, more complicated, solution.

Funders | Funder number |
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Sharma Thankachan | |

National Science Foundation | CCF-1217338, CNS-1318294, CCF-1514383 |

Israel Science Foundation | 897/13 |

## Keywords

- Distance oracles
- Near neighbor search
- Snippets
- Text indexing