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In this paper we study the fundamental problem of maintaining a dynamic collection of strings under the following operations: concat - concatenates two strings, split - splits a string into two at a given position, compare - finds the…

Data Structures and Algorithms · Computer Science 2016-04-11 Paweł Gawrychowski , Adam Karczmarz , Tomasz Kociumaka , Jakub Łącki , Piotr Sankowski

Efficient optimal prefix coding has long been accomplished via the Huffman algorithm. However, there is still room for improvement and exploration regarding variants of the Huffman problem. Length-limited Huffman coding, useful for many…

Information Theory · Computer Science 2007-07-13 Michael B. Baer

This paper investigates to what extent one can improve reinforcement learning algorithms. Our study is split in three parts. First, our analysis shows that the classical asymptotic convergence rate $O(1/\sqrt{N})$ is pessimistic and can be…

Machine Learning · Computer Science 2021-10-25 Othmane Mounjid , Charles-Albert Lehalle

The longest common substring problem consists in finding a longest string that appears as a (contiguous) substring of two input strings. We consider the dynamic variant of this problem, in which we are to maintain two dynamic strings $S$…

Data Structures and Algorithms · Computer Science 2026-04-09 Panagiotis Charalampopoulos , Paweł Gawrychowski , Karol Pokorski

In Gapped String Indexing, the goal is to compactly represent a string $S$ of length $n$ such that for any query consisting of two strings $P_1$ and $P_2$, called patterns, and an integer interval $[\alpha, \beta]$, called gap range, we can…

Data Structures and Algorithms · Computer Science 2024-03-06 Philip Bille , Inge Li Gørtz , Moshe Lewenstein , Solon P. Pissis , Eva Rotenberg , Teresa Anna Steiner

The suffix array and the suffix tree are the two most fundamental data structures for string processing. For a length-$n$ text, however, they use $\Theta(n \log n)$ bits of space, which is often too costly. To address this, Grossi and…

Data Structures and Algorithms · Computer Science 2023-04-20 Dominik Kempa , 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

We describe a data structure that stores a string $S$ in space similar to that of its Lempel-Ziv encoding and efficiently supports access, rank and select queries. These queries are fundamental for implementing succinct and compressed data…

Data Structures and Algorithms · Computer Science 2014-12-03 Djamal Belazzougui , Travis Gagie , Paweł Gawrychowski , Juha Kärkkäinen , Alberto Ordóñez , Simon J. Puglisi , Yasuo Tabei

We show that both the Lempel Ziv 77- and the 78-factorization of a text of length $n$ on an integer alphabet of size $\sigma$ can be computed in $O(n \lg \lg \sigma)$ time (linear time if we allow randomization) using $O(n \lg \sigma)$ bits…

Data Structures and Algorithms · Computer Science 2016-05-31 Dominik Köppl , Kunihiko Sadakane

We consider two natural problems about nondeterministic finite automata. First, given such an automaton M of n states, and a length l, does M accept a word of length l? We show that the classic problem of triangle-free graph recognition…

Formal Languages and Automata Theory · Computer Science 2018-02-14 Aaron Potechin , Jeffrey Shallit

In this paper, a fully compressed pattern matching problem is studied. The compression is represented by straight-line programs (SLPs), i.e. a context-free grammars generating exactly one string; the term fully means that both the pattern…

Data Structures and Algorithms · Computer Science 2013-06-26 Artur Jeż

We consider the problem of indexing a string $t$ of length $n$ to report the occurrences of a query pattern $p$ containing $m$ characters and $j$ wildcards. Let $occ$ be the number of occurrences of $p$ in $t$, and $\sigma$ the size of the…

Data Structures and Algorithms · Computer Science 2012-09-07 Philip Bille , Inge Li Goertz , Hjalte Wedel Vildhøj , Søren Vind

Efficient methods for storing and querying are critical for scaling high-order n-gram language models to large corpora. We propose a language model based on compressed suffix trees, a representation that is highly compact and can be easily…

Computation and Language · Computer Science 2016-08-17 Ehsan Shareghi , Matthias Petri , Gholamreza Haffari , Trevor Cohn

We revisit the problem of finding shortest unique substring (SUS) proposed recently by [6]. We propose an optimal $O(n)$ time and space algorithm that can find an SUS for every location of a string of size $n$. Our algorithm significantly…

Data Structures and Algorithms · Computer Science 2014-01-14 Atalay Mert İleri , M. Oğuzhan Külekci , Bojian Xu

Indexing highly repetitive texts - such as genomic databases, software repositories and versioned text collections - has become an important problem since the turn of the millennium. A relevant compressibility measure for repetitive texts…

Data Structures and Algorithms · Computer Science 2020-12-17 Travis Gagie , Gonzalo Navarro , Nicola Prezza

We study the problem of estimating the size of the maximum matching in the sublinear-time setting. This problem has been extensively studied, with several known upper and lower bounds. A notable result by Behnezhad (FOCS 2021) established a…

Data Structures and Algorithms · Computer Science 2026-02-17 Vihan Shah

Squares (fragments of the form $xx$, for some string $x$) are arguably the most natural type of repetition in strings. The basic algorithmic question concerning squares is to check if a given string of length $n$ is square-free, that is,…

Data Structures and Algorithms · Computer Science 2023-03-14 Jonas Ellert , Paweł Gawrychowski , Garance Gourdel

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

Repeat finding in strings has important applications in subfields such as computational biology. The challenge of finding the longest repeats covering particular string positions was recently proposed and solved by \.{I}leri et al., using a…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-01-28 Yun Tian , Bojian Xu

In this work, we consider the Submodular Maximization under Knapsack (SMK) constraint problem over the ground set of size $n$. The problem recently attracted a lot of attention due to its applications in various domains of combination…

Data Structures and Algorithms · Computer Science 2024-05-22 Canh V. Pham