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标题：Space Efficient Construction of Lyndon Arrays in Linear Time
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作者：Philip Bille ; Jonas Ellert ; Johannes Fischer 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2020
卷号：168
页码：14:1-14:18
DOI：10.4230/LIPIcs.ICALP.2020.14
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：Given a string S of length n, its Lyndon array identifies for each suffix S[i..n] the next lexicographically smaller suffix S[j..n], i.e. the minimal index j > i with S[i..n] â» S[j..n]. Apart from its plain (n logâ,, n)-bit array representation, the Lyndon array can also be encoded as a succinct parentheses sequence that requires only 2n bits of space. While linear time construction algorithms for both representations exist, it has previously been unknown if the same time bound can be achieved with less than Î©(n lg n) bits of additional working space. We show that, in fact, o(n) additional bits are sufficient to compute the succinct 2n-bit version of the Lyndon array in linear time. For the plain (n logâ,, n)-bit version, we only need ð'ª(1) additional words to achieve linear time. Our space efficient construction algorithm makes the Lyndon array more accessible as a fundamental data structure in applications like full-text indexing.
关键词：String algorithms; string suffixes; succinct data structures; Lyndon word; Lyndon array; nearest smaller values; nearest smaller suffixes