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Related papers: On the approximation ratio of LZ-End to LZ77

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Lyndon factorization and Lempel-Ziv (LZ) factorization are both important tools for analysing the structure and complexity of strings, but their combinatorial structure is very different. In this paper, we establish the first direct…

Data Structures and Algorithms · Computer Science 2020-12-08 Juha Kärkkäinen , Dominik Kempa , Yuto Nakashima , Simon J. Puglisi , Arseny M. Shur

We present a new, simple, and efficient approach for computing the Lempel-Ziv (LZ77) factorization of a string in linear time, based on suffix arrays. Computational experiments on various data sets show that our approach constantly…

Data Structures and Algorithms · Computer Science 2013-01-21 Keisuke Goto , Hideo Bannai

We propose algorithms computing the semi-greedy Lempel-Ziv 78 (LZ78), the Lempel-Ziv Double (LZD), and the Lempel-Ziv-Miller-Wegman (LZMW) factorizations in linear time for integer alphabets. For LZD and LZMW, we additionally propose data…

Data Structures and Algorithms · Computer Science 2024-09-24 Dominik Köppl

The Lempel-Ziv 77 (LZ77) factorization is a fundamental compression scheme widely used in text processing and data compression. In this work, we investigate the time complexity of maintaining the LZ77 factorization of a dynamic string. By…

Data Structures and Algorithms · Computer Science 2025-10-28 Itai Boneh , Shay Golan , Matan Kraus

Lempel-Ziv (LZ77) factorization is a fundamental problem in string processing: Greedily partition a given string $T$ from left to right into blocks (called phrases) so that each phrase is either the leftmost occurrence of a letter or the…

Data Structures and Algorithms · Computer Science 2025-06-19 Dominik Kempa , Tomasz Kociumaka

We introduce a new approach to LZ77 factorization that uses O(n/d) words of working space and O(dn) time for any d >= 1 (for polylogarithmic alphabet sizes). We also describe carefully engineered implementations of alternative approaches to…

Data Structures and Algorithms · Computer Science 2020-12-11 Juha Kärkkäinen , Dominik Kempa , Simon J. Puglisi

Computing the LZ factorization (or LZ77 parsing) of a string is a computational bottleneck in many diverse applications, including data compression, text indexing, and pattern discovery. We describe new linear time LZ factorization…

Data Structures and Algorithms · Computer Science 2020-12-11 Juha Kärkkäinen , Dominik Kempa , Simon J. Puglisi

Lempel-Ziv (LZ77 or, briefly, LZ) is one of the most effective and widely-used compressors for repetitive texts. However, the existing efficient methods computing the exact LZ parsing have to use linear or close to linear space to index the…

Data Structures and Algorithms · Computer Science 2020-05-12 Dmitry Kosolobov , Daniel Valenzuela , Gonzalo Navarro , Simon J. Puglisi

We present a new algorithm for computing the Lempel-Ziv Factorization (LZ77) of a given string of length $N$ in linear time, that utilizes only $N\log N + O(1)$ bits of working space, i.e., a single integer array, for constant size integer…

Data Structures and Algorithms · Computer Science 2013-10-08 Keisuke Goto , Hideo Bannai

We raise the question of approximating the compressibility of a string with respect to a fixed compression scheme, in sublinear time. We study this question in detail for two popular lossless compression schemes: run-length encoding (RLE)…

Data Structures and Algorithms · Computer Science 2007-06-11 Sofya Raskhodnikova , Dana Ron , Ronitt Rubinfeld , Adam Smith

An LZ-like factorization of a string divides it into factors, each being either a single character or a copy of a preceding substring. While grammar-based compression schemes support efficient random access with space linear in the…

Data Structures and Algorithms · Computer Science 2026-01-22 Hiroki Shibata , Yuto Nakashima , Yutaro Yamaguchi , Shunsuke Inenaga

For decades, computing the LZ factorization (or LZ77 parsing) of a string has been a requisite and computationally intensive step in many diverse applications, including text indexing and data compression. Many algorithms for LZ77 parsing…

Data Structures and Algorithms · Computer Science 2020-12-11 Juha Kärkkäinen , Dominik Kempa , Simon J. Puglisi

Relative Lempel-Ziv (RLZ) parsing is a dictionary compression method in which a string $S$ is compressed relative to a second string $R$ (called the reference) by parsing $S$ into a sequence of substrings that occur in $R$. RLZ is…

Data Structures and Algorithms · Computer Science 2022-08-25 Philip Bille , Inge Li Gørtz , Simon J. Puglisi , Simon R. Tarnow

We consider the communication complexity of the Hamming distance of two strings. Bille et al. [SPIRE 2018] considered the communication complexity of the longest common prefix (LCP) problem in the setting where the two parties have their…

Data Structures and Algorithms · Computer Science 2021-04-02 Shiori Mitsuya , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

We introduce height-bounded LZ encodings (LZHB), a new family of compressed representations that are variants of Lempel-Ziv parsings with a focus on bounding the worst-case access time to arbitrary positions in the text directly via the…

Data Structures and Algorithms · Computer Science 2024-04-26 Hideo Bannai , Mitsuru Funakoshi , Diptarama Hendrian , Myuji Matsuda , Simon J. Puglisi

The Lempel--Ziv 78 (LZ78) factorization is a well-studied technique for data compression. It and its derivatives are used in compression formats such as "compress" or "gif". Although most research focuses on the factorization of plain data,…

Data Structures and Algorithms · Computer Science 2025-12-22 Hiroki Shibata , Dominik Köppl

Lossless data compression has been widely studied in computer science. One of the most widely used lossless data compressions is Lempel-Zip(LZ) 77 parsing, which achieves a high compression ratio. Bidirectional (a.k.a. macro) parsing is a…

Data Structures and Algorithms · Computer Science 2018-12-12 Takaaki Nishimoto , Yasuo Tabei

This paper investigates the size in bits of the LZ77 encoding, which is the most popular and efficient variant of the Lempel-Ziv encodings used in data compression. We prove that, for a wide natural class of variable-length encoders for…

Discrete Mathematics · Computer Science 2018-01-10 Dmitry Kosolobov

We show how to compress string dictionaries using the Lempel-Ziv (LZ78) data compression algorithm. Our approach is validated experimentally on dictionaries of up to 1.5 GB of uncompressed text. We achieve compression ratios often…

Data Structures and Algorithms · Computer Science 2013-05-06 Julian Arz , Johannes Fischer

Lempel-Ziv-Double (LZD) is a variation of the LZ78 compression scheme that achieves better compression on repetitive datasets. Nevertheless, prior research has identified computational inefficiencies and a weakness in its compressibility…

Data Structures and Algorithms · Computer Science 2025-05-05 Linus Götz , Dominik Köppl
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