Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH scholarly article en Kempa, Dominik; Policriti, Alberto; Prezza, Nicola; Rotenberg, Eva http://www.dagstuhl.de/lipics License
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String Attractors: Verification and Optimization

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Abstract

String attractors [STOC 2018] are combinatorial objects recently introduced to unify all known dictionary compression techniques in a single theory. A set Gamma subseteq [1..n] is a k-attractor for a string S in Sigma^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 Gamma. 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 |Sigma| in O(sqrt[3+epsilon]{log n}) for some constant epsilon > 0, despite the problem being NP-hard for large Sigma.

BibTeX - Entry

@InProceedings{kempa_et_al:LIPIcs:2018:9515,
  author =	{Dominik Kempa and Alberto Policriti and Nicola Prezza and Eva Rotenberg},
  title =	{{String Attractors: Verification and Optimization}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{52:1--52:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Yossi Azar and Hannah Bast and Grzegorz Herman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9515},
  URN =		{urn:nbn:de:0030-drops-95153},
  doi =		{10.4230/LIPIcs.ESA.2018.52},
  annote =	{Keywords: Dictionary compression, String attractors, Set cover}
}

Keywords: Dictionary compression, String attractors, Set cover
Seminar: 26th Annual European Symposium on Algorithms (ESA 2018)
Issue date: 2018
Date of publication: 2018


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