@inproceedings{8c5fe45de07f41219fcedca252cff6e8,

title = "Space efficient construction of Lyndon arrays in linear time",

abstract = "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] S[j..n]. Apart from its plain (n log2 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 Ω(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 log2 n)-bit version, we only need O(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.",

keywords = "Lyndon array, Lyndon word, Nearest smaller suffixes, Nearest smaller values, String algorithms, String suffixes, Succinct data structures",

author = "Philip Bille and Jonas Ellert and Johannes Fischer and G{\o}rtz, {Inge Li} and Florian Kurpicz and {Ian Munro}, J. and Eva Rotenberg",

year = "2020",

month = jun,

day = "1",

doi = "10.4230/LIPIcs.ICALP.2020.14",

language = "English",

series = "Leibniz International Proceedings in Informatics, LIPIcs",

publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",

pages = "14:1----14:18",

editor = "Artur Czumaj and Anuj Dawar and Emanuela Merelli",

booktitle = "Proceedings of 47th International Colloquium on Automata, Languages and Programming",

note = "47<sup>th</sup> International Colloquium on Automata, Languages, and Programming, ICALP 2020 ; Conference date: 08-07-2020 Through 11-07-2020",

}