String attractors: Verification and optimization

Dominik Kempa, Alberto Policriti, Nicola Prezza, Eva Rotenberg

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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 ∈ Σn 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 languageEnglish
Title of host publicationProceedings of 26th European Symposium on Algorithms
Number of pages13
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Publication date1 Aug 2018
ISBN (Print)9783959770811
Publication statusPublished - 1 Aug 2018
Event26th Annual European Symposium on Algorithms - Helsinki, Finland
Duration: 20 Aug 201822 Aug 2018


Conference26th Annual European Symposium on Algorithms


  • Dictionary compression
  • Set cover
  • String attractors


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