English
Related papers

Related papers: Optimal Time Random Access to Grammar-Compressed S…

200 papers

In the last decades, the necessity to process massive amounts of textual data fueled the development of compressed text indexes: data structures efficiently answering queries on a given text while occupying space proportional to the…

Data Structures and Algorithms · Computer Science 2024-09-24 Dominik Kempa , Tomasz Kociumaka

Let $S$ be a string of length $n$ over an alphabet $\Sigma$ and let $Q$ be a subset of $\Sigma$ of size $q \geq 2$. The 'co-occurrence problem' is to construct a compact data structure that supports the following query: given an integer $w$…

Data Structures and Algorithms · Computer Science 2022-11-11 Philip Bille , Inge Li Gørtz , Tord Stordalen

The representation of a dynamic ordered set of $n$ integer keys drawn from a universe of size $m$ is a fundamental data structuring problem. Many solutions to this problem achieve optimal time but take polynomial space, therefore preserving…

Data Structures and Algorithms · Computer Science 2020-03-27 Giulio Ermanno Pibiri , Rossano Venturini

Suppose an oracle knows a string $S$ that is unknown to us and that we want to determine. The oracle can answer queries of the form "Is $s$ a substring of $S$?". In 1995, Skiena and Sundaram showed that, in the worst case, any algorithm…

Data Structures and Algorithms · Computer Science 2021-10-20 Gabriele Fici , Nicola Prezza , Rossano Venturini

Given a string $T$ of length $n$ over an alphabet $\Sigma\subset \{1,2,\ldots,n^{O(1)}\}$ of size $\sigma$, we are to preprocess $T$ so that given a range $[i,j]$, we can return a representation of a shortest string over $\Sigma$ that is…

Data Structures and Algorithms · Computer Science 2021-06-04 Golnaz Badkobeh , Panagiotis Charalampopoulos , Dmitry Kosolobov , Solon P. Pissis

A well-known fact in the field of lossless text compression is that high-order entropy is a weak model when the input contains long repetitions. Motivated by this, decades of research have generated myriads of so-called dictionary…

Data Structures and Algorithms · Computer Science 2020-12-17 Dominik Kempa , Nicola Prezza

We consider the problem of efficiently designing sets (codes) of equal-length DNA strings (words) that satisfy certain combinatorial constraints. This problem has numerous motivations including DNA computing and DNA self-assembly. Previous…

Data Structures and Algorithms · Computer Science 2007-05-23 Ming-Yang Kao , Manan Sanghi , Robert Schweller

Let $\D = $$ \{d_1,d_2,...d_D\}$ be a given set of $D$ string documents of total length $n$, our task is to index $\D$, such that the $k$ most relevant documents for an online query pattern $P$ of length $p$ can be retrieved efficiently. We…

Data Structures and Algorithms · Computer Science 2012-04-03 Wing-Kai Hon , Rahul Shah , Sharma V. Thankachan

In this paper we describe compressed indexes that support pattern matching queries for strings with wildcards. For a constant size alphabet our data structure uses $O(n\log^{\varepsilon}n)$ bits for any $\varepsilon>0$ and reports all…

Data Structures and Algorithms · Computer Science 2014-01-06 Moshe Lewenstein , Yakov Nekrich , Jeffrey Scott Vitter

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

We consider the problem of storing a dynamic string $S$ over an alphabet $\Sigma=\{\,1,\ldots,\sigma\,\}$ in compressed form. Our representation supports insertions and deletions of symbols and answers three fundamental queries:…

Data Structures and Algorithms · Computer Science 2015-07-27 J. Ian Munro , Yakov Nekrich

We study the fundamental problem of finding the best string to represent a given set, in the form of the Closest String problem: Given a set $X \subseteq \Sigma^d$ of $n$ strings, find the string $x^*$ minimizing the radius of the smallest…

Computational Complexity · Computer Science 2023-05-30 Amir Abboud , Nick Fischer , Elazar Goldenberg , Karthik C. S. , Ron Safier

Binary jumbled pattern matching asks to preprocess a binary string $S$ in order to answer queries $(i,j)$ which ask for a substring of $S$ that is of length $i$ and has exactly $j$ 1-bits. This problem naturally generalizes to…

Data Structures and Algorithms · Computer Science 2014-07-01 Travis Gagie , Danny Hermelin , Gad M. Landau , Oren Weimann

A key principle in string processing is local consistency: using short contexts to handle matching fragments of a string consistently. String synchronizing sets [Kempa, Kociumaka; STOC 2019] are an influential instantiation of this…

Data Structures and Algorithms · Computer Science 2026-02-13 Jonas Ellert , Tomasz Kociumaka

Given a string $T$ of length $N$, the goal of grammar compression is to construct a small context-free grammar generating only $T$. Among existing grammar compression methods, RePair (recursive paring) [Larsson and Moffat, 1999] is notable…

Data Structures and Algorithms · Computer Science 2018-11-06 Kensuke Sakai , Tatsuya Ohno , Keisuke Goto , Yoshimasa Takabatake , Tomohiro I , Hiroshi Sakamoto

In this paper we are interested in indexing texts for substring matching queries with one edit error. That is, given a text $T$ of $n$ characters over an alphabet of size $\sigma$, we are asked to build a data structure that answers the…

Data Structures and Algorithms · Computer Science 2014-08-25 Djamal Belazzougui

In the context of the compressed sensing problem, we propose a new ensemble of sparse random matrices which allow one (i) to acquire and compress a {\rho}0-sparse signal of length N in a time linear in N and (ii) to perfectly recover the…

Information Theory · Computer Science 2013-04-15 Maria Chiara Angelini , Federico Ricci-Tersenghi , Yoshiyuki Kabashima

We introduce the first grammar-compressed representation of a sequence that supports searches in time that depends only logarithmically on the size of the grammar. Given a text $T[1..u]$ that is represented by a (context-free) grammar of…

Data Structures and Algorithms · Computer Science 2011-10-21 Francisco Claude , Gonzalo Navarro

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

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