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Suppose that we are given two independent sets $I_b$ and $I_r$ of a graph such that $|I_b|=|I_r|$, and imagine that a token is placed on each vertex in $I_b$. Then, the sliding token problem is to determine whether there exists a sequence…

We present algorithms that run in linear time on pointer machines for a collection of problems, each of which either directly or indirectly requires the evaluation of a function defined on paths in a tree. These problems previously had…

Data Structures and Algorithms · Computer Science 2007-05-23 Adam L. Buchsbaum , Loukas Georgiadis , Haim Kaplan , Anne Rogers , Robert E. Tarjan , Jeffery R. Westbrook

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

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

We introduce a model for the retrieval of information hidden in legal texts. These are typically organised in a hierarchical (tree) structure, which a reader interested in a given provision needs to explore down to the "deepest" level…

Physics and Society · Physics 2024-09-17 Yanik-Pascal Förster , Alessia Annibale , Luca Gamberi , Evan Tzanis , Pierpaolo Vivo

Efficiently word storing and searching is an important task in computer science. An application space complexity, time complexity, and overall performance depend on this string data. Many word searching data structures and algorithms exist…

Data Structures and Algorithms · Computer Science 2019-11-06 Rahat Yeasin Emon , Sharmistha Chanda Tista

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

Recently, Cenzato et al.\ proposed a new text index, called the \emph{suffixient array}, which is a subset of the suffix array and supports locating a single pattern occurrence or finding its maximal exact matches (MEMs), assuming random…

Data Structures and Algorithms · Computer Science 2026-05-07 Paola Bonizzoni , Younan Gao , Brian Riccardi

An indexed sequence of strings is a data structure for storing a string sequence that supports random access, searching, range counting and analytics operations, both for exact matches and prefix search. String sequences lie at the core of…

Data Structures and Algorithms · Computer Science 2012-04-17 Roberto Grossi , Giuseppe Ottaviano

We describe an algorithm computing an optimal prefix free code from $N$ unsorted positive integer weights in time linear in the number of machine words holding those weights. This algorithm takes advantage of common non-algebraic…

Data Structures and Algorithms · Computer Science 2017-03-02 Jérémy Barbay

Suffix trees are an important data structure at the core of optimal solutions to many fundamental string problems, such as exact pattern matching, longest common substring, matching statistics, and longest repeated substring. Recent lines…

Data Structures and Algorithms · Computer Science 2022-08-31 Nicola Rizzo , Alexandru I. Tomescu , Alberto Policriti

A string is said to be closed if its length is one, or if it has a non-empty factor that occurs both as a prefix and as a suffix of the string, but does not occur elsewhere. The notion of closed words was introduced by [Fici, WORDS 2011].…

Data Structures and Algorithms · Computer Science 2024-10-01 Takuya Mieno , Shun Takahashi , Kazuhisa Seto , Takashi Horiyama

Natural language text corpora are often available as sets of syntactically parsed trees. A wide range of expressive tree queries are possible over such parsed trees that open a new avenue in searching over natural language text. They not…

Databases · Computer Science 2012-08-02 Pirooz Chubak , Davood Rafiei

We study a new variant of the string matching problem called cross-document string matching, which is the problem of indexing a collection of documents to support an efficient search for a pattern in a selected document, where the pattern…

Data Structures and Algorithms · Computer Science 2012-06-21 Gregory Kucherov , Yakov Nekrich , Tatiana Starikovskaya

In this paper we present novel algorithmic techniques with a O(H(N)+N/H(N)) time complexity for performing several types of queries and updates on general rooted trees, binary search trees and lists of size N. For rooted trees we introduce…

Data Structures and Algorithms · Computer Science 2013-03-25 Mugurel Ionut Andreica

We give an algorithm to enumerate the results on trees of monadic second-order (MSO) queries represented by nondeterministic tree automata. After linear time preprocessing (in the input tree), we can enumerate answers with linear delay (in…

Databases · Computer Science 2019-08-28 Antoine Amarilli , Pierre Bourhis , Stefan Mengel , Matthias Niewerth

We describe how, given a text $T [1..n]$ and a positive constant $\epsilon$, we can build a simple $O (z \log n)$-space index, where $z$ is the number of phrases in the LZ77 parse of $T$, such that later, given a pattern $P [1..m]$, in $O…

Data Structures and Algorithms · Computer Science 2022-12-06 Nick Fagan , Jorge Hermo González , Travis Gagie

An optimal binary search tree for an access sequence on elements is a static tree that minimizes the total search cost. Constructing perfectly optimal binary search trees is expensive so the most efficient algorithms construct almost…

Data Structures and Algorithms · Computer Science 2018-06-28 Mordecai Golin , John Iacono , Stefan Langerman , J. Ian Munro , Yakov Nekrich

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

Consider the following generalization of the classic binary search problem: a searcher is required to find a hidden vertex $x$ in a tree $T$. To do so, they iteratively perform queries to an oracle, each about a chosen vertex $v$. After…

Data Structures and Algorithms · Computer Science 2025-10-01 Michał Szyfelbein