English
Related papers

Related papers: Self-Index Based on LZ77

200 papers

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

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

Text indexing is a classical algorithmic problem that has been studied for over four decades: given a text $T$, pre-process it off-line so that, later, we can quickly count and locate the occurrences of any string (the query pattern) in $T$…

Data Structures and Algorithms · Computer Science 2020-12-15 Nicola Prezza

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

The advent of massive datasets (and the consequent design of high-performing distributed storage systems) have reignited the interest of the scientific and engineering community towards the design of lossless data compressors which achieve…

Information Theory · Computer Science 2013-07-16 Andrea Farruggia , Paolo Ferragina , Antonio Frangioni , Rossano Venturini

We present RCT, a new compact data structure to represent trajectories of objects. It is based on a relative compression technique called Relative Lempel-Ziv (RLZ), which compresses sequences by applying an LZ77 encoding with respect to an…

Data Structures and Algorithms · Computer Science 2018-10-16 Nieves R. Brisaboa , Travis Gagie , Adrián Gómez-Brandón , Gonzalo Navarro , José R. Paramá

Today there are many universal compression algorithms, but in most cases is for specific data better using specific algorithm - JPEG for images, MPEG for movies, etc. For textual documents there are special methods based on PPM algorithm or…

Information Theory · Computer Science 2008-12-18 Jan Platos , Jiri Dvorsky

Grammar-based compression is a popular and powerful approach to compressing repetitive texts but until recently its relatively poor time-space trade-offs during real-life construction made it impractical for truly massive datasets such as…

Data Structures and Algorithms · Computer Science 2020-07-21 Travis Gagie , Tomohiro I , Giovanni Manzini , Gonzalo Navarro , Hiroshi Sakamoto , Louisa Seelbach Benkner , Yoshimasa Takabatake

Most of the fastest-growing string collections today are repetitive, that is, most of the constituent documents are similar to many others. As these collections keep growing, a key approach to handling them is to exploit their…

Information Retrieval · Computer Science 2017-05-22 Travis Gagie , Aleksi Hartikainen , Kalle Karhu , Juha Kärkkäinen , Gonzalo Navarro , Simon J. Puglisi , Jouni Sirén

We study the approximate string matching and regular expression matching problem for the case when the text to be searched is compressed with the Ziv-Lempel adaptive dictionary compression schemes. We present a time-space trade-off that…

Data Structures and Algorithms · Computer Science 2007-05-23 Philip Bille , Rolf Fagerberg , Inge Li Goertz

Web archives, query and proxy logs, and so on, can all be very large and highly repetitive; and are accessed only sporadically and partially, rather than continually and holistically. This type of data is ideal for compression-based…

Information Theory · Computer Science 2016-03-01 Matthias Petri , Alistair Moffat , P. C. Nagesh , Anthony Wirth

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

In this paper, we show that the LZ77 factorization of a text T {\in\Sigma^n} can be computed in O(R log n) bits of working space and O(n log R) time, R being the number of runs in the Burrows-Wheeler transform of T reversed. For extremely…

Data Structures and Algorithms · Computer Science 2015-10-22 Nicola Prezza , Alberto Policriti

This paper presents an algorithm for the modification of data compressed using LZ-End, a derivate of LZ77, without prior decompression. The performance of the algorithm and the impact of the modifications on the compression ratio is…

Data Structures and Algorithms · Computer Science 2020-07-14 Daniel Roodt , Ulrich Speidel , Vimal Kumar , Ryan K. L. Ko

We propose and study a family of universal sequential probability assignments on individual sequences, based on the incremental parsing procedure of the Lempel-Ziv (LZ78) compression algorithm. We show that the normalized log loss under any…

Information Theory · Computer Science 2025-12-15 Naomi Sagan , Tsachy Weissman

Data compression continues to evolve, with traditional information theory methods being widely used for compressing text, images, and videos. Recently, there has been growing interest in leveraging Generative AI for predictive compression…

Information Theory · Computer Science 2024-09-24 Swathi Shree Narashiman , Nitin Chandrachoodan

With current hardware and software, a standard computer can now hold in RAM an index for approximate pattern matching on about half a dozen human genomes. Sequencing technologies have improved so quickly, however, that scientists will soon…

Data Structures and Algorithms · Computer Science 2013-07-25 Hector Ferrada , Travis Gagie , Tommi Hirvola , Simon J. Puglisi

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

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

An optimal index solving top-k document retrieval [Navarro and Nekrich, SODA12] takes O(m + k) time for a pattern of length m, but its space is at least 80n bytes for a collection of n symbols. We reduce it to 1.5n to 3n bytes, with…

Data Structures and Algorithms · Computer Science 2012-11-26 Roberto Konow , Gonzalo Navarro