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A deterministic BSP algorithm for constructing the suffix array of a given string is presented, based on a technique which we call accelerated sampling. It runs in optimal O(n/p) local computation and communication, and requires a near…

Distributed, Parallel, and Cluster Computing · Computer Science 2013-02-26 Matthew Felice Pace , Alexander Tiskin

We give the first algorithm for adaptive alphabetic prefix-free coding that is worst-case optimal in terms of time and compression when $\sigma \in o \left( \frac{n^{1 / 2}}{\log n} \right)$, where $\sigma$ is the size of the alphabet and…

Data Structures and Algorithms · Computer Science 2026-01-08 Travis Gagie

We consider the problems of computing maximal palindromes and distinct palindromes in a trie. A trie is a natural generalization of a string, which can be seen as a single-path tree. There is a linear-time offline algorithm to compute…

Data Structures and Algorithms · Computer Science 2026-01-26 Hiroki Shibata , Mitsuru Funakoshi , Takuya Mieno , Masakazu Ishihata , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

Sublinear time quantum algorithms have been established for many fundamental problems on strings. This work demonstrates that new, faster quantum algorithms can be designed when the string is highly compressible. We focus on two popular and…

Data Structures and Algorithms · Computer Science 2023-02-15 Daniel Gibney , Sharma V. Thankachan

When comparing the fastest algorithm for computing the largest simulation preorder over Kripke structures with the one for labeled transition systems (LTS), there is a noticeable time and space complexity blow-up proportional to the size of…

Formal Languages and Automata Theory · Computer Science 2023-07-11 Lukáš Holík , Jiří Šimáček

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

The Block Tree is a recently proposed data structure that reaches compression close to Lempel-Ziv while supporting efficient direct access to text substrings. In this paper we show how a self-index can be built on top of a Block Tree so…

Data Structures and Algorithms · Computer Science 2017-10-11 Gonzalo Navarro

We present an efficient algorithm for computing the LZ78 factorization of a text, where the text is represented as a straight line program (SLP), which is a context free grammar in the Chomsky normal form that generates a single string.…

Data Structures and Algorithms · Computer Science 2013-05-27 Hideo Bannai , Shunsuke Inenaga , Masayuki Takeda

Lyndon factorization and Lempel-Ziv (LZ) factorization are both important tools for analysing the structure and complexity of strings, but their combinatorial structure is very different. In this paper, we establish the first direct…

Data Structures and Algorithms · Computer Science 2020-12-08 Juha Kärkkäinen , Dominik Kempa , Yuto Nakashima , Simon J. Puglisi , Arseny M. Shur

Two strings of equal length are said to parameterized match if there is a bijection that maps the characters of one string to those of the other string, so that two strings become identical. The parameterized pattern matching problem is,…

Data Structures and Algorithms · Computer Science 2018-08-06 Noriki Fujisato , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

Suffix tree (and the closely related suffix array) are fundamental structures capturing all substrings of a given text essentially by storing all its suffixes in the lexicographical order. In some applications, we work with a subset of $b$…

Data Structures and Algorithms · Computer Science 2016-08-03 Paweł Gawrychowski , Tomasz Kociumaka

Compression techniques that support fast random access are a core component of any information system. Current state-of-the-art methods group documents into fixed-sized blocks and compress each block with a general-purpose adaptive…

Data Structures and Algorithms · Computer Science 2015-03-19 Christopher Hoobin , Simon J. Puglisi , Justin Zobel

Simple and fast decoding is one of the main advantages of LZ77-type text encoding used in many popular file compressors such as gzip and 7zip. With the recent introduction of external memory algorithms for Lempel-Ziv factorization there is…

Data Structures and Algorithms · Computer Science 2020-12-11 Djamal Belazzougui , Juha Kärkkäinen , Dominik Kempa , Simon J. Puglisi

The problem of constructing optimal factoring automata arises in the context of unification factoring for the efficient execution of logic programs. Given an ordered set of $n$ strings of length $m$, the problem is to construct a trie-like…

Data Structures and Algorithms · Computer Science 2024-04-04 Thomas Erlebach , Kleitos Papadopoulos

In a \emph{weighted sequence}, for every position of the sequence and every letter of the alphabet a probability of occurrence of this letter at this position is specified. Weighted sequences are commonly used to represent imprecise or…

Data Structures and Algorithms · Computer Science 2017-08-28 Carl Barton , Tomasz Kociumaka , Chang Liu , Solon P. Pissis , Jakub Radoszewski

The abelian pattern matching problem consists in finding all substrings of a text which are permutations of a given pattern. This problem finds application in many areas and can be solved in linear time by a naive sliding window approach.…

Data Structures and Algorithms · Computer Science 2018-03-08 Simone Faro , Arianna Pavone

We introduce a new algorithm for constructing the generalized suffix array of a collection of highly similar strings. As a first step, we construct a compressed representation of the matching statistics of the collection with respect to a…

Data Structures and Algorithms · Computer Science 2024-04-16 Zsuzsanna Lipták , Francesco Masillo , Simon J. Puglisi

We derive upper and lower bounds on the overall compression ratio of the 1978 Lempel-Ziv (LZ78) algorithm, applied independently to $k$-blocks of a finite individual sequence. Both bounds are given in terms of normalized empirical entropies…

Information Theory · Computer Science 2025-06-17 Neri Merhav

Suffix arrays encode the lexicographical order of all suffixes of a text and are often combined with the Longest Common Prefix array (LCP) to simulate navigational queries on the suffix tree in reduced space. In space-critical applications…

Data Structures and Algorithms · Computer Science 2017-11-02 Nicola Prezza

The suffix array, perhaps the most important data structure in modern string processing, is often augmented with the longest common prefix (LCP) array which stores the lengths of the LCPs for lexicographically adjacent suffixes of a string.…

Data Structures and Algorithms · Computer Science 2017-02-27 Juha Kärkkäinen , Marcin Piątkowski , Simon J. Puglisi