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In many real-world database systems, a large fraction of the data is represented by strings: sequences of letters over some alphabet. This is because strings can easily encode data arising from different sources. It is often crucial to…

Data Structures and Algorithms · Computer Science 2024-07-17 Lorraine A. K. Ayad , Grigorios Loukides , Solon P. Pissis

This paper proposes a novel entropy encoding technique for lossless data compression. Representing a message string by its lexicographic index in the permutations of its symbols results in a compressed version matching Shannon entropy of…

Information Theory · Computer Science 2017-03-24 Abu Bakar Siddique

The Burrows-Wheeler transform (BWT) is a string transformation that enhances string indexing and compressibility. Cotumaccio and Prezza [SODA '21] extended this transformation to nondeterministic finite automata (NFAs) through…

Data Structures and Algorithms · Computer Science 2025-03-11 Ruben Becker , Nicola Cotumaccio , Sung-Hwan Kim , Nicola Prezza , Carlo Tosoni

The Burrows-Wheeler Transform (BWT) has been an essential tool in text compression and indexing. First introduced in 1994, it went on to provide the backbone for the first encoding of the classic suffix tree data structure in space close to…

Data Structures and Algorithms · Computer Science 2020-02-19 Jason Bentley , Daniel Gibney , Sharma V. Thankachan

Two decades ago, a breakthrough in indexing string collections made it possible to represent them within their compressed space while at the same time offering indexed search functionalities. As this new technology permeated through…

Data Structures and Algorithms · Computer Science 2022-11-28 Gonzalo Navarro

Constraint Programming is a powerful paradigm to model and solve combinatorial problems. While there are many kinds of constraints, the table constraint is perhaps the most significant-being the most well-studied and has the ability to…

Databases · Computer Science 2022-03-23 Soufia Bennai , Kamala Amroun , Samir Loudni , Abdelkader Ouali

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

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

In 1-bit compressed sensing, the aim is to estimate a $k$-sparse unit vector $x\in S^{n-1}$ within an $\epsilon$ error (in $\ell_2$) from minimal number of linear measurements that are quantized to just their signs, i.e., from measurements…

Information Theory · Computer Science 2023-10-13 Namiko Matsumoto , Arya Mazumdar

Consider the set of all sequences of $n$ outcomes, each taking one of $m$ values, that satisfy a number of linear constraints. If $m$ is fixed while $n$ increases, most sequences that satisfy the constraints result in frequency vectors…

Information Theory · Computer Science 2016-11-18 Kostas N. Oikonomou , Peter D. Grunwald

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

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

This paper proposed a storing approach for trie structures, called coordinate hash trie. The basic idea is using a global hash table with a special hash function to store all edges of a trie. For a trie with $n$ nodes and an alphabet with…

Data Structures and Algorithms · Computer Science 2023-03-28 Yuxuan Dong

We give a new successor data structure which improves upon the index size of the P\v{a}tra\c{s}cu-Thorup data structures, reducing the index size from $O(n w^{4/5})$ bits to $O(n \log w)$ bits, with optimal probe complexity. Alternatively,…

Data Structures and Algorithms · Computer Science 2013-06-18 Sarel Cohen , Amos Fiat , Moshik Hershcovitch , Haim Kaplan

In this paper we study lower bounds for the fundamental problem of text indexing with mismatches and differences. In this problem we are given a long string of length $n$, the "text", and the task is to preprocess it into a data structure…

Data Structures and Algorithms · Computer Science 2018-12-24 Vincent Cohen-Addad , Laurent Feuilloley , Tatiana Starikovskaya

A range of recent works addresses the problem of compression of sequence of tokens into a shorter sequence of real-valued vectors to be used as inputs instead of token embeddings or key-value cache. These approaches are focused on reduction…

Computation and Language · Computer Science 2025-06-24 Yuri Kuratov , Mikhail Arkhipov , Aydar Bulatov , Mikhail Burtsev

The problem of finding factors of a text string which are identical or similar to a given pattern string is a central problem in computer science. A generalised version of this problem consists in implementing an index over the text to…

Data Structures and Algorithms · Computer Science 2016-02-04 Carl Barton , Tomasz Kociumaka , Solon P. Pissis , Jakub Radoszewski

We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…

Information Theory · Computer Science 2011-04-05 Paul M. B. Vitányi

The boom of genomic sequencing makes compression of set of sequences inescapable. This underlies the need for multi-string indexing data structures that helps compressing the data. The most prominent example of such data structures is the…

Data Structures and Algorithms · Computer Science 2021-11-18 Bastien Cazaux , Eric Rivals

Suppose that we are given a string $s$ of length $n$ over an alphabet $\{0,1,\ldots,n^{O(1)}\}$ and $\delta$ is the string complexity of $s$, a known compression measure. We describe an index on $s$ with $O(\delta\log\frac{n}{\delta})$…

Data Structures and Algorithms · Computer Science 2026-04-15 Dmitry Kosolobov