License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2021.35
URN: urn:nbn:de:0030-drops-136809
URL: https://drops.dagstuhl.de/opus/volltexte/2021/13680/
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Gibney, Daniel ; Thankachan, Sharma V.

Finding an Optimal Alphabet Ordering for Lyndon Factorization Is Hard

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LIPIcs-STACS-2021-35.pdf (0.7 MB)


Abstract

This work establishes several strong hardness results on the problem of finding an ordering on a string’s alphabet that either minimizes or maximizes the number of factors in that string’s Lyndon factorization. In doing so, we demonstrate that these ordering problems are sufficiently complex to model a wide variety of ordering constraint satisfaction problems (OCSPs). Based on this, we prove that (i) the decision versions of both the minimization and maximization problems are NP-complete, (ii) for both the minimization and maximization problems there does not exist a constant approximation algorithm running in polynomial time under the Unique Game Conjecture and (iii) there does not exist an algorithm to solve the minimization problem in time poly(|T|) ⋅ 2^o(σlog σ) for a string T over an alphabet of size σ under the Exponential Time Hypothesis (essentially the brute force approach of trying every alphabet order is hard to improve significantly).

BibTeX - Entry

@InProceedings{gibney_et_al:LIPIcs.STACS.2021.35,
  author =	{Gibney, Daniel and Thankachan, Sharma V.},
  title =	{{Finding an Optimal Alphabet Ordering for Lyndon Factorization Is Hard}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{35:1--35:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13680},
  URN =		{urn:nbn:de:0030-drops-136809},
  doi =		{10.4230/LIPIcs.STACS.2021.35},
  annote =	{Keywords: Lyndon Factorization, String Algorithms, Burrows-Wheeler Transform}
}

Keywords: Lyndon Factorization, String Algorithms, Burrows-Wheeler Transform
Collection: 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)
Issue Date: 2021
Date of publication: 10.03.2021


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