Faster compact on-line Lempel-ziv factorization

Jun'ichi Yamamoto, Tomohiro I, Hideo Bannai, Shunsuke Inenaga, Masayuki Takeda

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Citations (Scopus)

Abstract

We present a new on-line algorithm for computing the Lempel-Ziv factorization of a string that runs in O(N logN) time and uses only O(N log σ) bits of working space, where N is the length of the string and σ 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 log3N) time (Okanohara & Sadakane 2009) or O(N log2N) 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{n (log logm)(log logN)/log log logN , √ logm/log logm o})time and O(mlogN) bits of space.

Original languageEnglish
Title of host publication31st International Symposium on Theoretical Aspects of Computer Science, STACS 2014
EditorsNatacha Portier, Ernst W. Mayr
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages675-686
Number of pages12
ISBN (Electronic)9783939897651
DOIs
Publication statusPublished - Mar 1 2014
Event31st International Symposium on Theoretical Aspects of Computer Science, STACS 2014 - Lyon, France
Duration: Mar 5 2014Mar 8 2014

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume25
ISSN (Print)1868-8969

Other

Other31st International Symposium on Theoretical Aspects of Computer Science, STACS 2014
CountryFrance
CityLyon
Period3/5/143/8/14

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All Science Journal Classification (ASJC) codes

  • Software

Cite this

Yamamoto, J., I, T., Bannai, H., Inenaga, S., & Takeda, M. (2014). Faster compact on-line Lempel-ziv factorization. In N. Portier, & E. W. Mayr (Eds.), 31st International Symposium on Theoretical Aspects of Computer Science, STACS 2014 (pp. 675-686). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 25). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.STACS.2014.675