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.ESA.2022.86
URN: urn:nbn:de:0030-drops-170249
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17024/
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Tiskin, Alexander

Fast RSK Correspondence by Doubling Search

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Abstract

The Robinson-Schensted-Knuth (RSK) correspondence is a fundamental concept in combinatorics and representation theory. It is defined as a certain bijection between permutations and pairs of Young tableaux of a given order. We consider the RSK correspondence as an algorithmic problem, along with the closely related k-chain problem. We give a simple, direct description of the symmetric RSK algorithm, which is implied by the k-chain algorithms of Viennot and of Felsner and Wernisch. We also show how the doubling search of Bentley and Yao can be used as a subroutine by the symmetric RSK algorithm, replacing the default binary search. Surprisingly, such a straightforward replacement improves the asymptotic worst-case running time for the RSK correspondence that has been best known since 1998. A similar improvement also holds for the average running time of RSK on uniformly random permutations.

BibTeX - Entry

@InProceedings{tiskin:LIPIcs.ESA.2022.86,
  author =	{Tiskin, Alexander},
  title =	{{Fast RSK Correspondence by Doubling Search}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{86:1--86:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17024},
  URN =		{urn:nbn:de:0030-drops-170249},
  doi =		{10.4230/LIPIcs.ESA.2022.86},
  annote =	{Keywords: combinatorics of permutations, Robinson-Schensted-Knuth correspondence, k-chains, RSK algorithm}
}

Keywords: combinatorics of permutations, Robinson-Schensted-Knuth correspondence, k-chains, RSK algorithm
Collection: 30th Annual European Symposium on Algorithms (ESA 2022)
Issue Date: 2022
Date of publication: 01.09.2022

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