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Related papers: LZ-End Parsing in Compressed Space

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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

We investigate the relations between different variants of the LZ77 parsing existing in the literature. All of them are defined as greedily constructed parsings encoding each phrase by reference to a string occurring earlier in the input.…

Information Theory · Computer Science 2018-05-24 Dmitry Kosolobov , Arseny M. Shur

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

Shannon's entropy is a clear lower bound for statistical compression. The situation is not so well understood for dictionary-based compression. A plausible lower bound is $b$, the least number of phrases of a general bidirectional parse of…

Data Structures and Algorithms · Computer Science 2019-10-29 Gonzalo Navarro , Carlos Ochoa , Nicola Prezza

We consider the problem of decompressing the Lempel--Ziv 77 representation of a string $S$ of length $n$ using a working space as close as possible to the size $z$ of the input. The folklore solution for the problem runs in $O(n)$ time but…

Data Structures and Algorithms · Computer Science 2019-11-05 Philip Bille , Mikko Berggren Ettienne , Travis Gagie , Inge Li Gørtz , Nicola Prezza

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

We study the problem of supporting queries on a string $S$ of length $n$ within a space bounded by the size $\gamma$ of a string attractor for $S$. Recent works showed that random access on $S$ can be supported in optimal…

Data Structures and Algorithms · Computer Science 2018-12-24 Nicola Prezza

Mauer et al. [A Lempel-Ziv-style Compression Method for Repetitive Texts, PSC 2017] proposed a hybrid text compression method called LZ-LFS which has both features of Lempel-Ziv 77 factorization and longest first substitution. They showed…

Data Structures and Algorithms · Computer Science 2018-06-14 Akihiro Nishi , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

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

In this paper, we present the following results: (1) We propose a new \emph{dynamic compressed index} of $O(w)$ space, that supports searching for a pattern $P$ in the current text in $O(|P| f(M,w) + \log w \log |P| \log^* M (\log N + \log…

Data Structures and Algorithms · Computer Science 2016-04-07 Takaaki Nishimoto , I Tomohiro , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

Compression refers to encoding data using bits, so that the representation uses as few bits as possible. Compression could be lossless: i.e. encoded data can be recovered exactly from its representation) or lossy where the data is…

Information Theory · Computer Science 2012-10-19 Narayana Santhanam , Dharmendra Modha

Given two positions $i$ and $j$ in a string $T$ of length $N$, a longest common extension (LCE) query asks for the length of the longest common prefix between suffixes beginning at $i$ and $j$. A compressed LCE data structure is a data…

Data Structures and Algorithms · Computer Science 2016-11-22 Tomohiro I

The \emph{longest common extension} (\emph{LCE}) problem is to preprocess a given string $w$ of length $n$ so that the length of the longest common prefix between suffixes of $w$ that start at any two given positions is answered quickly. In…

Data Structures and Algorithms · Computer Science 2017-02-27 Yuka Tanimura , Takaaki Nishimoto , Hideo Bannai , Shunsuke Inenaga , Masayuki Takeda

We show that both the Lempel Ziv 77- and the 78-factorization of a text of length $n$ on an integer alphabet of size $\sigma$ can be computed in $O(n \lg \lg \sigma)$ time (linear time if we allow randomization) using $O(n \lg \sigma)$ bits…

Data Structures and Algorithms · Computer Science 2016-05-31 Dominik Köppl , Kunihiko Sadakane

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

In this paper we investigate the problem of building a static data structure that represents a string s using space close to its compressed size, and allows fast access to individual characters of s. This type of structures was investigated…

Computational Complexity · Computer Science 2012-05-04 Shiteng Chen , Elad Verbin , Wei Yu

In this paper, we describe a new type of match between a pattern and a text that aren't necessarily maximal in the query, but still contain useful matching information: locally maximal exact matches (LEMs). There are usually a large amount…

Data Structures and Algorithms · Computer Science 2025-05-22 Ahsan Sanaullah , Degui Zhi , Shaojie Zhang

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

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

Given a string $S$, the \emph{compressed indexing problem} is to preprocess $S$ into a compressed representation that supports fast \emph{substring queries}. The goal is to use little space relative to the compressed size of $S$ while…

Data Structures and Algorithms · Computer Science 2018-01-10 Philip Bille , Mikko Berggren Ettienne , Inge Li Gørtz , Hjalte Wedel Vildhøj