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.CPM.2021.4
URN: urn:nbn:de:0030-drops-139554
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13955/
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Adamson, Duncan ; Gusev, Vladimir V. ; Potapov, Igor ; Deligkas, Argyrios

Ranking Bracelets in Polynomial Time

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LIPIcs-CPM-2021-4.pdf (0.8 MB)

Abstract

The main result of the paper is the first polynomial-time algorithm for ranking bracelets. The time-complexity of the algorithm is O(k²⋅ n⁴), where k is the size of the alphabet and n is the length of the considered bracelets. The key part of the algorithm is to compute the rank of any word with respect to the set of bracelets by finding three other ranks: the rank over all necklaces, the rank over palindromic necklaces, and the rank over enclosing apalindromic necklaces. The last two concepts are introduced in this paper. These ranks are key components to our algorithm in order to decompose the problem into parts. Additionally, this ranking procedure is used to build a polynomial-time unranking algorithm.

BibTeX - Entry

@InProceedings{adamson_et_al:LIPIcs.CPM.2021.4,
  author =	{Adamson, Duncan and Gusev, Vladimir V. and Potapov, Igor and Deligkas, Argyrios},
  title =	{{Ranking Bracelets in Polynomial Time}},
  booktitle =	{32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021)},
  pages =	{4:1--4:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-186-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{191},
  editor =	{Gawrychowski, Pawe{\l} and Starikovskaya, Tatiana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13955},
  URN =		{urn:nbn:de:0030-drops-139554},
  doi =		{10.4230/LIPIcs.CPM.2021.4},
  annote =	{Keywords: Bracelets, Ranking, Necklaces}
}

Keywords: Bracelets, Ranking, Necklaces
Collection: 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021)
Issue Date: 2021
Date of publication: 30.06.2021

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