Let T be a text of length n on an alphabet Σ of size σ, and let H0 be the zero-order empirical entropy of T. We show that the LZ77 factorization of T can be computed in nH0+o(nlogσ)+O(σlogn) bits of working space with an online algorithm running in O(nlogn) time. Previous space-efficient online solutions either work in compact space and O(nlogn) time, or in succinct space and O(nlog3n) time.
Fast online Lempel-Ziv factorization in compressed space / Policriti, Alberto; Prezza, Nicola. - String Processing and Information Retrieval 22nd International Symposium, SPIRE 2015, London, UK, September 1-4, 2015, Proceedings, (2015), pp. 13-20. (22nd International Symposium on String Processing and Information Retrieval, SPIRE 2015, London, UK, September 1-4, 2015). [10.1007/978-3-319-23826-5_2].
Fast online Lempel-Ziv factorization in compressed space
PREZZA, Nicola
2015
Abstract
Let T be a text of length n on an alphabet Σ of size σ, and let H0 be the zero-order empirical entropy of T. We show that the LZ77 factorization of T can be computed in nH0+o(nlogσ)+O(σlogn) bits of working space with an online algorithm running in O(nlogn) time. Previous space-efficient online solutions either work in compact space and O(nlogn) time, or in succinct space and O(nlog3n) time.
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