Kempa, Dominik ;
Policriti, Alberto ;
Prezza, Nicola ;
Rotenberg, Eva
String Attractors: Verification and Optimization
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 kattractor 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 kattractor is NPhard for k >= 3, but polylogarithmic approximations can be found using reductions from dictionary compressors. It is easy to reduce the kattractor problem to a setcover 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 kattractor in nearoptimal time and how to quickly compute exact solutions. For example, we prove that a minimum 3attractor 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 NPhard 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 = {52:152:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770811},
ISSN = {18688969},
year = {2018},
volume = {112},
editor = {Yossi Azar and Hannah Bast and Grzegorz Herman},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9515},
URN = {urn:nbn:de:0030drops95153},
doi = {10.4230/LIPIcs.ESA.2018.52},
annote = {Keywords: Dictionary compression, String attractors, Set cover}
}
2018
Keywords: 

Dictionary compression, String attractors, Set cover 
Seminar: 

26th Annual European Symposium on Algorithms (ESA 2018)

Issue date: 

2018 
Date of publication: 

2018 