Lempel–Ziv Factorization Powered by Space Efficient Suffix Trees

Refining the r-index

“…We implemented in C++ the online LZ77 parsing algorithm of Theorem 6 (the source code is available at [22]). There are lots of work for LZ77 parsing (e.g., see [31][32][33][34][35][36][37][38][39][40][41][42][43] and references therein). Among them we choose the ones whose implementations potentially work in the peak RAM usage smaller than n lg σ + n lg n bits and compare with our method.…”

Non-Overlapping LZ77 Factorization and LZ78 Substring Compression Queries with Suffix Trees

“…For LZSS, this means that a factor F x must occur at least once in F 1 • • • F x−1 . Given a text T of length n whose characters are drawn from an integer alphabet of size σ = n O (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. In this article, we obtain the non-overlapping LZSS factorization with similar techniques and within the same space boundaries: Theorem 1.…”

“…Despite this increased complexity compared to the overlapping LZSS factorization, the non-overlapping factorization can be computed with the suffix tree in O(n lg σ) time using O(n lg n) bits of space ( [31] [APL16]). Here, we adapt the algorithms of (Fischer et al [4] [Section 3]) computing the overlapping LZSS factorization to compute the non-overlapping factorization by following the approach of Gusfield [31]. Our goal is to compute the coding of the factors, i.e., the referred position and the length of each factor (cf.…”

“…Here, we provide the first non-trivial solutions for LZ78, again with the help of several suffix tree representations: is the number of computed LZ78 factors and ∈ (0, 1] is a selectable constant. In the last result, we need additionally the n lg σ bits of space for the read-only text during the queries if there is any character of the alphabet omitted in the text (otherwise, we can then simulate a text access with the function head as described in [4]).…”

Compact Data Structures for Shortest Unique Substring Queries

“…Our Contribution In this paper, we propose the following two data structures: (A) A data structure of size 2n + 2m + o(n) bits answering an interval SUS query in O(occ) time, where m is the number of minimal unique substrings of the input string 3 , and occ is the number of SUSs of T for the respective query interval (Theorem 1). (B) A data structure of size ⌈(log 2 3 + 1)n⌉ + o(n) bits answering a point SUS query in O(occ) time, where occ is the number of SUSs of T for the respective query point (Theorem 2).…”