## Abstract

String attractors [STOC 2018] are combinatorial objects recently introduced to unify all known dictionary compression techniques in a single theory. A set γ ⊆ [1.n] is a k-attractor for a string S ∈ Σ^{n} if and only if every distinct substring of S of length at most k has an occurrence crossing at least one of the positions in γ. Finding the smallest k-attractor is NP-hard for k ≥ 3, but polylogarithmic approximations can be found using reductions from dictionary compressors. It is easy to reduce the k-attractor problem to a set-cover instance where the string's positions are interpreted as sets of substrings. The main result of this paper is a much more powerful reduction based on the truncated suffix tree. Our new characterization of the problem leads to more efficient algorithms for string attractors: we show how to check the validity and minimality of a k-attractor in near-optimal time and how to quickly compute exact solutions. For example, we prove that a minimum 3-attractor can be found in O(n) time when |Σ| ∈ O(^{3+ϵ}√log n) for some constant ϵ > 0, despite the problem being NP-hard for large Σ.

Original language | English |
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Title of host publication | Proceedings of 26th European Symposium on Algorithms |

Number of pages | 13 |

Volume | 112 |

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

Publication date | 1 Aug 2018 |

ISBN (Print) | 9783959770811 |

DOIs | |

Publication status | Published - 1 Aug 2018 |

Event | 26th Annual European Symposium on Algorithms - Helsinki, Finland Duration: 20 Aug 2018 → 22 Aug 2018 |

### Conference

Conference | 26th Annual European Symposium on Algorithms |
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Country/Territory | Finland |

City | Helsinki |

Period | 20/08/2018 → 22/08/2018 |

## Keywords

- Dictionary compression
- Set cover
- String attractors