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oai:drops-oai.dagstuhl.de:4497 2024-03-06T10:35:08Z ddc:004 open_access

Faster Compact On-Line Lempel-Ziv Factorization Yamamoto, Jun'ichi I, Tomohiro Bannai, Hideo Inenaga, Shunsuke Takeda, Masayuki Lempel-Ziv Factorization String Index We present a new on-line algorithm for computing the Lempel-Ziv factorization of a string that runs in O(N.log(N)) time and uses only O(N.log(s)) bits of working space, where N is the length of the string and s is the size of the alphabet. This is a notable improvement compared to the performance of previous on-line algorithms using the same order of working space but running in either O(N.log^3(N)) time [Okanohara and Sadakane, 2009] or O(N.log^2(N)) time [Starikovskaya, 2012]. The key to our new algorithm is in the utilization of an elegant but less popular index structure called Directed Acyclic Word Graphs, or DAWGs [Blumer et al., 1985]. We also present an opportunistic variant of our algorithm, which, given the run length encoding of size m of a string of length N, computes the Lempel-Ziv factorization of the string on-line, in O(m.min{log(log(m)).log(log(N))/(log(log(log(N)))), (log(m))^{1/2}/(log(log(m)))^{1/2})}) time and O(m.log(N)) bits of space. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Jun'ichi Yamamoto and Tomohiro I and Hideo Bannai and Shunsuke Inenaga and Masayuki Takeda 2014 Is Part Of LIPIcs, Volume 25, 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2014.675 urn:nbn:de:0030-drops-44976 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2014.675 eng https://creativecommons.org/licenses/by/3.0/legalcode