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.
@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/entities/document/10.4230/LIPIcs.ESA.2022.86}, 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} }
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