Fast online Lempel-Ziv factorization in compressed space

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.