English
Related papers

Related papers: Small-space encoding LCE data structure with const…

200 papers

We study the problem of supporting queries on a string $S$ of length $n$ within a space bounded by the size $\gamma$ of a string attractor for $S$. Recent works showed that random access on $S$ can be supported in optimal…

Data Structures and Algorithms · Computer Science 2018-12-24 Nicola Prezza

Big data, encompassing extensive datasets, has seen rapid expansion, notably with a considerable portion being textual data, including strings and texts. Simple compression methods and standard data structures prove inadequate for…

Data Structures and Algorithms · Computer Science 2024-11-11 Takaaki Nishimoto , Yasuo Tabei

In this work, we consider pattern matching variants in small space, that is, in the read-only setting, where we want to bound the space usage on top of storing the strings. Our main contribution is a space-time trade-off for the Internal…

Data Structures and Algorithms · Computer Science 2024-04-29 Gabriel Bathie , Panagiotis Charalampopoulos , Tatiana Starikovskaya

We give algorithms that, given a straight-line program (SLP) with $g$ rules that generates (only) a text $T [1..n]$, builds within $O(g)$ space the Lempel-Ziv (LZ) parse of $T$ (of $z$ phrases) in time $O(n\log^2 n)$ or in time…

Data Structures and Algorithms · Computer Science 2023-10-11 Travis Gagie , Adrián Goga , Artur Jeż , Gonzalo Navarro

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

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

The Longest Common Subsequence (LCS) is a fundamental string similarity measure, and computing the LCS of two strings is a classic algorithms question. A textbook dynamic programming algorithm gives an exact algorithm in quadratic time, and…

Data Structures and Algorithms · Computer Science 2023-02-13 Xiaoyu He , Ray Li

Calculating the length of a longest common subsequence (LCS) of two strings $A$ and $B$ of length $n$ and $m$ is a classic research topic, with many worst-case oriented results known. We present two algorithms for LCS length calculation…

Data Structures and Algorithms · Computer Science 2014-05-22 Szymon Grabowski

Much research has been devoted to optimizing algorithms of the Lempel-Ziv (LZ) 77 family, both in terms of speed and memory requirements. Binary search trees and suffix trees (ST) are data structures that have been often used for this…

Data Structures and Algorithms · Computer Science 2016-11-17 Artur Ferreira , Arlindo Oliveira , Mario Figueiredo

Karpinski and Nekrich (2008) introduced the problem of parameterized range majority, which asks to preprocess a string of length $n$ such that, given the endpoints of a range, one can quickly find all the distinct elements whose relative…

Data Structures and Algorithms · Computer Science 2014-07-15 Djamal Belazzougui , Travis Gagie , Gonzalo Navarro

We introduce height-bounded LZ encodings (LZHB), a new family of compressed representations that are variants of Lempel-Ziv parsings with a focus on bounding the worst-case access time to arbitrary positions in the text directly via the…

Data Structures and Algorithms · Computer Science 2024-04-26 Hideo Bannai , Mitsuru Funakoshi , Diptarama Hendrian , Myuji Matsuda , Simon J. Puglisi

It is well-known that, given a probability distribution over $n$ characters, in the worst case it takes (\Theta (n \log n)) bits to store a prefix code with minimum expected codeword length. However, in this paper we first show that, for…

Data Structures and Algorithms · Computer Science 2009-05-20 Travis Gagie , Gonzalo Navarro , Yakov Nekrich

We show that the compressed suffix array and the compressed suffix tree for a string of length $n$ over an integer alphabet of size $\sigma\leq n$ can both be built in $O(n)$ (randomized) time using only $O(n\log\sigma)$ bits of working…

Data Structures and Algorithms · Computer Science 2016-05-24 Djamal Belazzougui

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

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

Karpinski and Nekrich (2008) introduced the problem of parameterized range majority, which asks us to preprocess a string of length $n$ such that, given the endpoints of a range, one can quickly find all the distinct elements whose relative…

Data Structures and Algorithms · Computer Science 2016-06-15 Djamal Belazzougui , Travis Gagie , J. Ian Munro , Gonzalo Navarro , Yakov Nekrich

Sparse suffix sorting is the problem of sorting $b=o(n)$ suffixes of a string of length $n$. Efficient sparse suffix sorting algorithms have existed for more than a decade. Despite the multitude of works and their justified claims for…

Data Structures and Algorithms · Computer Science 2024-07-08 Lorraine A. K. Ayad , Grigorios Loukides , Solon P. Pissis , Hilde Verbeek

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

Longest common substring (LCS), longest palindrome substring (LPS), and Ulam distance (UL) are three fundamental string problems that can be classically solved in near linear time. In this work, we present sublinear time quantum algorithms…

Quantum Physics · Physics 2023-12-29 François Le Gall , Saeed Seddighin

We consider an index data structure for similar strings. The generalized suffix tree can be a solution for this. The generalized suffix tree of two strings $A$ and $B$ is a compacted trie representing all suffixes in $A$ and $B$. It has…

Data Structures and Algorithms · Computer Science 2013-05-09 Joong Chae Na , Heejin Park , Maxime Crochemore , Jan Holub , Costas S. Iliopoulos , Laurent Mouchard , Kunsoo Park