2 Search Results for "Tiskin, Alexander"


Document
Fast RSK Correspondence by Doubling Search

Authors: Alexander Tiskin

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)


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.

Cite as

Alexander Tiskin. Fast RSK Correspondence by Doubling Search. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 86:1-86:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@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-dev.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}
}
Document
Bounded-Length Smith-Waterman Alignment

Authors: Alexander Tiskin

Published in: LIPIcs, Volume 143, 19th International Workshop on Algorithms in Bioinformatics (WABI 2019)


Abstract
Given a fixed alignment scoring scheme, the bounded length (respectively, bounded total length) Smith-Waterman alignment problem on a pair of strings of lengths m, n, asks for the maximum alignment score across all substring pairs, such that the first substring’s length (respectively, the sum of the two substrings' lengths) is above the given threshold w. The latter problem was introduced by Arslan and Eğecioğlu under the name "local alignment with length threshold". They proposed a dynamic programming algorithm solving the problem in time O(mn^2), and also an approximation algorithm running in time O(rmn), where r is a parameter controlling the accuracy of approximation. We show that both these problems can be solved exactly in time O(mn), assuming a rational scoring scheme; furthermore, this solution can be used to obtain an exact algorithm for the normalised bounded total length Smith - Waterman alignment problem, running in time O(mn log n). Our algorithms rely on the techniques of fast window-substring alignment and implicit unit-Monge matrix searching, developed previously by the author and others.

Cite as

Alexander Tiskin. Bounded-Length Smith-Waterman Alignment. In 19th International Workshop on Algorithms in Bioinformatics (WABI 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 143, pp. 16:1-16:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Copy BibTex To Clipboard

@InProceedings{tiskin:LIPIcs.WABI.2019.16,
  author =	{Tiskin, Alexander},
  title =	{{Bounded-Length Smith-Waterman Alignment}},
  booktitle =	{19th International Workshop on Algorithms in Bioinformatics (WABI 2019)},
  pages =	{16:1--16:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-123-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{143},
  editor =	{Huber, Katharina T. and Gusfield, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2019.16},
  URN =		{urn:nbn:de:0030-drops-110461},
  doi =		{10.4230/LIPIcs.WABI.2019.16},
  annote =	{Keywords: sequence alignment, local alignment, Smith, Waterman alignment, matrix searching}
}
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