License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CPM.2020.2
URN: urn:nbn:de:0030-drops-121270
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12127/
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Alzamel, Mai ; Conte, Alessio ; Denzumi, Shuhei ; Grossi, Roberto ; Iliopoulos, Costas S. ; Kurita, Kazuhiro ; Wasa, Kunihiro

Finding the Anticover of a String

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LIPIcs-CPM-2020-2.pdf (0.6 MB)

Abstract

A k-anticover of a string x is a set of pairwise distinct factors of x of equal length k, such that every symbol of x is contained into an occurrence of at least one of those factors. The existence of a k-anticover can be seen as a notion of non-redundancy, which has application in computational biology, where they are associated with various non-regulatory mechanisms. In this paper we address the complexity of the problem of finding a k-anticover of a string x if it exists, showing that the decision problem is NP-complete on general strings for k ≥ 3. We also show that the problem admits a polynomial-time solution for k=2. For unbounded k, we provide an exact exponential algorithm to find a k-anticover of a string of length n (or determine that none exists), which runs in O*(min {3^{(n-k)/3)}, ((k(k+1))/2)^{n/(k+1)) time using polynomial space.

BibTeX - Entry

@InProceedings{alzamel_et_al:LIPIcs:2020:12127,
  author =	{Mai Alzamel and Alessio Conte and Shuhei Denzumi and Roberto Grossi and Costas S. Iliopoulos and Kazuhiro Kurita and Kunihiro Wasa},
  title =	{{Finding the Anticover of a String}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{2:1--2:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{Inge Li G{\o}rtz and Oren Weimann},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12127},
  URN =		{urn:nbn:de:0030-drops-121270},
  doi =		{10.4230/LIPIcs.CPM.2020.2},
  annote =	{Keywords: Anticover, String algorithms, Stringology, NP-complete}
}

Keywords: Anticover, String algorithms, Stringology, NP-complete
Collection: 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)
Issue Date: 2020
Date of publication: 09.06.2020

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