English
Related papers

Related papers: Sublinear Algorithms for Approximating String Comp…

200 papers

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

The properties of maximum Lempel-Ziv complexity strings are studied for the binary case. A comparison between MLZs and random strings is carried out. The length profile of both type of sequences show different distribution functions. The…

Chaotic Dynamics · Physics 2013-11-05 C. A. J. Nunes , E. Estevez-Rams , B. Aragón Fernández , R. Lora Serrano

The paper proposes an improved error-resilient Lempel-Ziv'77 (LZ'77) algorithm employing an adaptive amount of parity bits for error protection. It is a modified version of error resilient algorithm LZRS'77, proposed recently, which uses a…

Information Theory · Computer Science 2008-04-21 Tomaz Korosec , Saso Tomazic

The compression-complexity trade-off of lossy compression algorithms that are based on a random codebook or a random database is examined. Motivated, in part, by recent results of Gupta-Verd\'{u}-Weissman (GVW) and their underlying…

Information Theory · Computer Science 2009-04-23 Chris Gioran , Ioannis Kontoyiannis

Motivated by the imminent growth of massive, highly redundant genomic databases, we study the problem of compressing a string database while simultaneously supporting fast random access, substring extraction and pattern matching to the…

Data Structures and Algorithms · Computer Science 2012-11-01 Travis Gagie , Paweł Gawrychowski , Christopher Hoobin , Simon J. Puglisi

This article gives a self-contained analysis of the performance of the Lempel-Ziv compression algorithm on (hidden) Markovian sources. Specifically we include a full proof of the assertion that the compression rate approaches the entropy…

Information Theory · Computer Science 2019-10-03 Madhu Sudan , David Xiang

This paper presents conditional versions of Lempel-Ziv (LZ) algorithm for settings where compressor and decompressor have access to the same side information. We propose a fixed-length-parsing LZ algorithm with side information, motivated…

Information Theory · Computer Science 2017-07-19 Yeohee Im , Sergio Verdú

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

In this paper we compare the difference in performance of two of the Prediction by Partial Matching (PPM) family of compressors (PPM$^*$ and the original Bounded PPM algorithm) and the Lempel-Ziv 78 (LZ) algorithm. We construct an infinite…

Data Structures and Algorithms · Computer Science 2021-01-21 Liam Jordon , Philippe Moser

The sensitivity of a string compression algorithm $C$ asks how much the output size $C(T)$ for an input string $T$ can increase when a single character edit operation is performed on $T$. This notion enables one to measure the robustness of…

Data Structures and Algorithms · Computer Science 2023-02-10 Tooru Akagi , Mitsuru Funakoshi , Shunsuke Inenaga

Here we study the complexity of string problems as a function of the size of a program that generates input. We consider straight-line programs (SLP), since all algorithms on SLP-generated strings could be applied to processing…

Data Structures and Algorithms · Computer Science 2007-05-23 Yury Lifshits

Despite consistently yielding the best compression on repetitive text collections, the Lempel-Ziv parsing has resisted all attempts at offering relevant guarantees on the cost to access an arbitrary symbol. This makes it less attractive for…

Data Structures and Algorithms · Computer Science 2024-04-24 Zsuzsanna Lipták , Francesco Masillo , Gonzalo Navarro

The well-known dictionary-based algorithms of the Lempel-Ziv (LZ) 77 family are the basis of several universal lossless compression techniques. These algorithms are asymmetric regarding encoding/decoding time and memory requirements, with…

Data Structures and Algorithms · Computer Science 2009-12-31 Artur Ferreira , Arlindo Oliveira , Mario Figueiredo

Unlike in statistical compression, where Shannon's entropy is a definitive lower bound, no such clear measure exists for the compressibility of repetitive sequences. Since statistical entropy does not capture repetitiveness, ad-hoc measures…

Data Structures and Algorithms · Computer Science 2021-01-18 Tomasz Kociumaka , Gonzalo Navarro , Nicola Prezza

Given a string $S$ of length $n$, the classic string indexing problem is to preprocess $S$ into a compact data structure that supports efficient subsequent pattern queries. In this paper we consider the basic variant where the pattern is…

Data Structures and Algorithms · Computer Science 2024-02-15 Philip Bille , Inge Li Gørtz , Teresa Anna Steiner

Shannon's entropy is a definitive lower bound for statistical compression. Unfortunately, no such clear measure exists for the compressibility of repetitive strings. Thus, ad hoc measures are employed to estimate the repetitiveness of…

Data Structures and Algorithms · Computer Science 2023-11-16 Giulia Bernardini , Gabriele Fici , Paweł Gawrychowski , Solon P. Pissis

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

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

We propose a new approach for calculating the Lempel-Ziv factorization of a string, based on run length encoding (RLE). We present a conceptually simple off-line algorithm based on a variant of suffix arrays, as well as an on-line algorithm…

Data Structures and Algorithms · Computer Science 2015-03-20 Jun'ichi Yamamoto , Hideo Bannai , Shunsuke Inenaga , Masayuki Takeda

Advances in DNA sequencing technology will soon result in databases of thousands of genomes. Within a species, individuals' genomes are almost exact copies of each other; e.g., any two human genomes are 99.9% the same. Relative Lempel-Ziv…

Data Structures and Algorithms · Computer Science 2011-11-08 Travis Gagie , Juha Kärkkäinen , Yakov Nekrich , Simon J. Puglisi