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Tries are among the most versatile and widely used data structures on words. They are pertinent to the (internal) structure of (stored) words and several splitting procedures used in diverse contexts ranging from document taxonomy to IP…

Probability · Mathematics 2012-09-20 Kevin Leckey , Ralph Neininger , Wojciech Szpankowski

Suffix trees are key and efficient data structure for solving string problems. A suffix tree is a compressed trie containing all the suffixes of a given text of length $n$ with a linear construction cost. In this work, we introduce an…

Data Structures and Algorithms · Computer Science 2024-06-04 Anas Al-okaily

The suffix trees are fundamental data structures for various kinds of string processing. The suffix tree of a text string $T$ of length $n$ has $O(n)$ nodes and edges, and the string label of each edge is encoded by a pair of positions in…

Data Structures and Algorithms · Computer Science 2023-12-06 Diptarama Hendrian , Takuya Takagi , Shunsuke Inenaga , Keisuke Goto , Mitsuru Funakoshi

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

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 layer-ordered heap (LOH) is a simple, recently proposed data structure used in optimal selection on $X+Y$, thealgorithm with the best known runtime for selection on $X_1+X_2+\cdots+X_m$, and the fastest method in practice for computing…

Data Structures and Algorithms · Computer Science 2020-08-18 Jake Pennington , Patrick Kreitzberg , Kyle Lucke , Oliver Serang

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

Countless variants of the Lempel-Ziv compression are widely used in many real-life applications. This paper is concerned with a natural modification of the classical pattern matching problem inspired by the popularity of such compression…

Data Structures and Algorithms · Computer Science 2011-04-22 Pawel Gawrychowski

Large-alphabet strings are common in scenarios such as information retrieval and natural-language processing. The efficient storage and processing of such strings usually introduces several challenges that are not witnessed in…

Data Structures and Algorithms · Computer Science 2024-05-03 Diego Arroyuelo , Gabriel Carmona , Héctor Larrañaga , Francisco Riveros , Carlos Eugenio Rojas-Morales , Erick Sepúlveda

A family of Lempel-Ziv factorizations is a well-studied string structure. The LZ-End factorization is a member of the family that achieved faster extraction of any substrings (Kreft & Navarro, TCS 2013). One of the interests for LZ-End…

Data Structures and Algorithms · Computer Science 2021-08-17 Takumi Ideue , Takuya Mieno , Mitsuru Funakoshi , Yuto Nakashima , Shunsuke Inenaga , Masayuki Takeda

We present the first thorough practical study of the Lempel-Ziv-78 and the Lempel-Ziv-Welch computation based on trie data structures. With a careful selection of trie representations we can beat well-tuned popular trie data structures like…

Data Structures and Algorithms · Computer Science 2017-06-12 Johannes Fischer , Dominik Köppl

We present a compressed representation of tries based on top tree compression [ICALP 2013] that works on a standard, comparison-based, pointer machine model of computation and supports efficient prefix search queries. Namely, we show how to…

Data Structures and Algorithms · Computer Science 2019-09-23 Philip Bille , Inge Li Gørtz , Paweł Gawrychowski , Gad M. Landau , Oren Weimann

We present an algorithm for computing the Lyndon factorization of a string that is given in grammar compressed form, namely, a Straight Line Program (SLP). The algorithm runs in $O(n^4 + mn^3h)$ time and $O(n^2)$ space, where $m$ is the…

Data Structures and Algorithms · Computer Science 2013-04-29 Tomohiro I , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

Given two strings $T$ and $S$ and a set of strings $P$, for each string $p \in P$, consider the unique substrings of $T$ that have $p$ as their prefix and $S$ as their suffix. Two problems then come to mind; the first problem being the…

Data Structures and Algorithms · Computer Science 2022-04-19 Laurentius Leonard , Ken Tanaka

One of the most famous and investigated lossless data-compression scheme is the one introduced by Lempel and Ziv about 40 years ago. This compression scheme is known as "dictionary-based compression" and consists of squeezing an input…

Data Structures and Algorithms · Computer Science 2008-02-07 Paolo Ferragina , Igor Nitto , Rossano Venturini

We study the complexity of constructing an optimal parsing $\varphi$ of a string ${\bf s} = s_1 \dots s_n$ under the constraint that given a position $p$ in the original text, and the LZ76-like (Lempel Ziv 76) encoding of $T$ based on…

Data Structures and Algorithms · Computer Science 2024-03-26 Ferdinando Cicalese , Francesca Ugazio

Given an approximation algorithm $A$, we want to find the input with the worst approximation ratio, i.e., the input for which $A$'s output's objective value is the worst possible compared to the optimal solution's objective value. Such hard…

Data Structures and Algorithms · Computer Science 2025-04-29 Eklavya Sharma

In this paper we present a really simple linear-time algorithm constructing a context-free grammar of size O(g log (N/g)) for the input string, where N is the size of the input string and g the size of the optimal grammar generating this…

Data Structures and Algorithms · Computer Science 2014-03-19 Artur Jeż

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

Suffix arrays and LCP arrays are one of the most fundamental data structures widely used for various kinds of string processing. We consider two problems for a read-only string of length $N$ over an integer alphabet $[1, \dots, \sigma]$ for…

Data Structures and Algorithms · Computer Science 2019-07-16 Keisuke Goto