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We consider the problem of {\em restructuring} compressed texts without explicit decompression. We present algorithms which allow conversions from compressed representations of a string $T$ produced by any grammar-based compression…

Data Structures and Algorithms · Computer Science 2011-07-15 Keisuke Goto , Shirou Maruyama , Shunsuke Inenaga , Hideo Bannai , Hiroshi Sakamoto , Masayuki Takeda

We present an algorithm which computes the Lempel-Ziv factorization of a word $W$ of length $n$ on an alphabet $\Sigma$ of size $\sigma$ online in the following sense: it reads $W$ starting from the left, and, after reading each $r =…

Data Structures and Algorithms · Computer Science 2012-12-03 Tatiana Starikovskaya

Grammar based compression, where one replaces a long string by a small context-free grammar that generates the string, is a simple and powerful paradigm that captures many popular compression schemes. In this paper, we present a novel…

Data Structures and Algorithms · Computer Science 2013-10-30 Philip Bille , Gad M. Landau , Rajeev Raman , Kunihiko Sadakane , Srinivasa Rao Satti , Oren Weimann

We present a unified framework for accelerating edit-distance computation between two compressible strings using straight-line programs. For two strings of total length $N$ having straight-line program representations of total size $n$, we…

Computational Complexity · Computer Science 2009-02-17 Danny Hermelin , Gad M. Landau , Shir Landau , Oren Weimann

We present an algorithm that computes the Lempel-Ziv decomposition in $O(n(\log\sigma + \log\log n))$ time and $n\log\sigma + \epsilon n$ bits of space, where $\epsilon$ is a constant rational parameter, $n$ is the length of the input…

Data Structures and Algorithms · Computer Science 2015-06-09 Dmitry Kosolobov

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

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 consider the problem of evaluating regular spanners over compressed documents, i.e., we wish to solve evaluation tasks directly on the compressed data, without decompression. As compressed forms of the documents we use straight-line…

Data Structures and Algorithms · Computer Science 2021-01-27 Markus L. Schmid , Nicole Schweikardt

We show that the compressed suffix array and the compressed suffix tree of a string $T$ can be built in $O(n)$ deterministic time using $O(n\log\sigma)$ bits of space, where $n$ is the string length and $\sigma$ is the alphabet size.…

Data Structures and Algorithms · Computer Science 2016-11-15 J. Ian Munro , Gonzalo Navarro , Yakov Nekrich

Given an LZW/LZ78 compressed text, we want to find an approximate occurrence of a given pattern of length m. The goal is to achieve time complexity depending on the size n of the compressed representation of the text instead of its length.…

Data Structures and Algorithms · Computer Science 2013-09-23 Pawel Gawrychowski , Damian Straszak

The LZ-End parsing [Kreft & Navarro, 2011] of an input string yields compression competitive with the popular Lempel-Ziv 77 scheme, but also allows for efficient random access. Kempa and Kosolobov showed that the parsing can be computed in…

Data Structures and Algorithms · Computer Science 2024-09-18 Patrick Dinklage

We study algorithms for approximating pairwise similarity matrices that arise in natural language processing. Generally, computing a similarity matrix for $n$ data points requires $\Omega(n^2)$ similarity computations. This quadratic…

Machine Learning · Computer Science 2022-04-28 Archan Ray , Nicholas Monath , Andrew McCallum , Cameron Musco

We present novel variants of fully online LCA (FOLCA), a fully online grammar compression that builds a straight line program (SLP) and directly encodes it into a succinct representation in an online manner. FOLCA enables a direct encoding…

Data Structures and Algorithms · Computer Science 2014-01-30 Shirou Maruyama , Yasuo Tabei

Classically, the edit distance of two length-$n$ strings can be computed in $O(n^2)$ time, whereas an $O(n^{2-\epsilon})$-time procedure would falsify the Orthogonal Vectors Hypothesis. If the edit distance does not exceed $k$, the running…

Data Structures and Algorithms · Computer Science 2023-11-06 Daniel Gibney , Ce Jin , Tomasz Kociumaka , Sharma V. Thankachan

We give an $\mathcal{O}(n \log n)$-time, $\mathcal{O}(n)$-space algorithm for factoring a string into the minimum number of palindromic substrings. That is, given a string $S [1..n]$, in $\mathcal{O}(n \log n)$ time our algorithm returns…

Data Structures and Algorithms · Computer Science 2020-12-15 Gabriele Fici , Travis Gagie , Juha Kärkkäinen , Dominik Kempa

The Karp-Rabin fingerprint of a string is a type of hash value that due to its strong properties has been used in many string algorithms. In this paper we show how to construct a data structure for a string $S$ of size $N$ compressed by a…

Data Structures and Algorithms · Computer Science 2013-05-17 Philip Bille , Patrick Hagge Cording , Inge Li Gørtz , Benjamin Sach , Hjalte Wedel Vildhøj , Søren Vind

A factorization $f_1, \ldots, f_m$ of a string $w$ of length $n$ is called a repetition factorization of $w$ if $f_i$ is a repetition, i.e., $f_i$ is a form of $x^kx'$, where $x$ is a non-empty string, $x'$ is a (possibly-empty) proper…

Data Structures and Algorithms · Computer Science 2024-08-09 Yuki Yonemoto , Shunsuke Inenaga

Internal Pattern Matching (IPM) queries on a text $T$, given two fragments $X$ and $Y$ of $T$ such that $|Y|<2|X|$, ask to compute all exact occurrences of $X$ within $Y$. IPM queries have been introduced by Kociumaka, Radoszewski, Rytter,…

Data Structures and Algorithms · Computer Science 2025-03-06 Anouk Duyster , Tomasz Kociumaka

A Straight-Line Program (SLP) for a string $T$ is a context-free grammar in Chomsky normal form that derives $T$ only, which can be seen as a compressed form of $T$. Kida et al.\ introduced collage systems [Theor. Comput. Sci., 2003] to…

Data Structures and Algorithms · Computer Science 2026-01-27 Soichiro Migita , Kyotaro Uehata , Tomohiro I

The compressed indexing problem is to preprocess a string $S$ of length $n$ into a compressed representation that supports pattern matching queries. That is, given a string $P$ of length $m$ report all occurrences of $P$ in $S$. We present…

Data Structures and Algorithms · Computer Science 2018-04-12 Anders Roy Christiansen , Mikko Berggren Ettienne