Computing Longest (Common) Lyndon Subsequences

Given a string T with length n whose characters are drawn from an ordered alphabet of size σ $$\sigma $$ , its longest Lyndon subsequence is a longest subsequence of T that is a Lyndon word. We propose algorithms for finding such a subsequence in O(n3) $$\mathcal {O}(n^3)$$ time with O(n) $$\mathcal...

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Bibliographic Details
Published inCombinatorial Algorithms Vol. 13270; pp. 128 - 142
Main Authors Bannai, Hideo, I, Tomohiro, Kociumaka, Tomasz, Köppl, Dominik, Puglisi, Simon J.
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 2022
Springer International Publishing
SeriesLecture Notes in Computer Science
Subjects
Dynamic programming
Lyndon word
Subsequence
Online AccessGet full text
ISBN3031066774
9783031066771
ISSN0302-9743
1611-3349
DOI10.1007/978-3-031-06678-8_10

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Summary:Given a string T with length n whose characters are drawn from an ordered alphabet of size σ $$\sigma $$ , its longest Lyndon subsequence is a longest subsequence of T that is a Lyndon word. We propose algorithms for finding such a subsequence in O(n3) $$\mathcal {O}(n^3)$$ time with O(n) $$\mathcal {O}(n)$$ space, or online in O(n3σ) $$\mathcal {O}(n^3 \sigma )$$ space and time. Our first result can be extended to find the longest common Lyndon subsequence of two strings of length n in O(n4σ) $$\mathcal {O}(n^4 \sigma )$$ time using O(n3) $$\mathcal {O}(n^3)$$ space.
Bibliography:Original Abstract: Given a string T with length n whose characters are drawn from an ordered alphabet of size σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}, its longest Lyndon subsequence is a longest subsequence of T that is a Lyndon word. We propose algorithms for finding such a subsequence in O(n3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {O}(n^3)$$\end{document} time with O(n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {O}(n)$$\end{document} space, or online in O(n3σ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {O}(n^3 \sigma )$$\end{document} space and time. Our first result can be extended to find the longest common Lyndon subsequence of two strings of length n in O(n4σ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {O}(n^4 \sigma )$$\end{document} time using O(n3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {O}(n^3)$$\end{document} space.
ISBN:3031066774
9783031066771
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-031-06678-8_10