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Longest Lyndon substring after edit. (English) Zbl 07286745
Navarro, Gonzalo (ed.) et al., 29th annual symposium on combinatorial pattern matching, CPM 2018, July 2–4, 2018, Qingdao, China. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik (ISBN 978-3-95977-074-3). LIPIcs – Leibniz International Proceedings in Informatics 105, Article 19, 10 p. (2018).
Summary: The longest Lyndon substring of a string \(T\) is the longest substring of \(T\) which is a Lyndon word. \(\operatorname{LLS}(T)\) denotes the length of the longest Lyndon substring of a string \(T\). In this paper, we consider computing \(\operatorname{LLS}(T')\) where \(T'\) is an edited string formed from \(T\). After \(O(n)\) time and space preprocessing, our algorithm returns \(\operatorname{LLS}(T')\) in \(O(\log n)\) time for any single character edit. We also consider a version of the problem with block edits, i.e., a substring of \(T\) is replaced by a given string of length \(l\). After \(O(n)\) time and space preprocessing, our algorithm returns \(\operatorname{LLS}(T')\) in \(O(l\log\sigma+ \log n)\) time for any block edit where \(\sigma\) is the number of distinct characters in \(T\). We can modify our algorithm so as to output all the longest Lyndon substrings of \(T'\) for both problems.
For the entire collection see [Zbl 1390.68025].

68W32 Algorithms on strings
Full Text: DOI
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