Abstract
We present algorithms computing the non-overlapping Lempel–Ziv-77 factorization and the longest previous non-overlapping factor table within small space in linear or near-linear time with the help of modern suffix tree representations fitting into limited space. With similar techniques, we show how to answer substring compression queries for the Lempel–Ziv-78 factorization with a possible logarithmic multiplicative slowdown depending on the used suffix tree representation.
Highlights
Given a text T of length n whose characters are drawn from an integer alphabet of size σ = nO(1), we want to study the problem of computing the non-overlapping LZSS factorization memory-efficiently with the aid of two suffix tree representations, which were used by Fischer et al [4] (Section 2.2) to compute the classic LZ77, LZSS, and LZ78 factorizations in linear time within the asymptotic space requirements of the respective suffix tree
We study the substring compression query problem [6], where the task is to compute the factorization of a given substring of the text in time related to the number of computed factors and possibly a logarithmic dependency on the text length
We used techniques introduced by Fischer et al [4], which work on the succinct suffix tree (SST) and the compressed suffix tree (CST), to tackle the non-overlapping LZSS factorization and the LZ78 substring compression query problem
Summary
Given a text T of length n whose characters are drawn from an integer alphabet of size σ = nO(1) , we want to study the problem of computing the non-overlapping LZSS factorization memory-efficiently with the aid of two suffix tree representations, which were used by Fischer et al [4] (Section 2.2) to compute the classic LZ77, LZSS, and LZ78 factorizations in linear time within the asymptotic space requirements of the respective suffix tree. . n] of length n whose characters are drawn from an integer alphabet with size σ = nO(1) , we can compute its non-overlapping LZSS factorization in O(e−1 n) time using (1 + e)n lg n + O(n) bits (excluding the read-only text T); or in O(n lge n) time using O(n lg σ ) bits, for a selectable constant e ∈
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