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Given a pattern string $P$ of length $n$ and a query string $T$ of length $m$, where the characters of $P$ and $T$ are drawn from an alphabet of size $\Delta$, the {\em exact string matching} problem consists of finding all occurrences of…

Data Structures and Algorithms · Computer Science 2015-10-01 Srikrishnan Divakaran

The longest common extension problem (LCE problem) is to construct a data structure for an input string $T$ of length $n$ that supports LCE$(i,j)$ queries. Such a query returns the length of the longest common prefix of the suffixes…

Data Structures and Algorithms · Computer Science 2015-04-13 Philip Bille , Inge Li Gørtz , Mathias Bæk Tejs Knudsen , Moshe Lewenstein , Hjalte Wedel Vildhøj

A Straight-Line Program (SLP) $G$ for a string $T$ is a context-free grammar (CFG) that derives $T$ only, which can be considered as a compressed representation of $T$. In this paper, we show how to encode $G$ in $n \lceil \lg N \rceil + (n…

Data Structures and Algorithms · Computer Science 2026-01-09 Akito Takasaka , Tomohiro I

Suppose we want to seek the longest common subsequences (LCSs) of two strings as informative patterns that explain the relationship between the strings. The dynamic programming algorithm gives us a table from which all LCSs can be extracted…

Data Structures and Algorithms · Computer Science 2025-05-23 Yoshifumi Sakai

For a static array A of n ordered objects, a range minimum query asks for the position of the minimum between two specified array indices. We show how to preprocess A into a scheme of size 2n+o(n) bits that allows to answer range minimum…

Data Structures and Algorithms · Computer Science 2009-12-02 Johannes Fischer

The circular dictionary matching problem is an extension of the classical dictionary matching problem where every string in the dictionary is interpreted as a circular string: after reading the last character of a string, we can move back…

Data Structures and Algorithms · Computer Science 2025-04-07 Nicola Cotumaccio

Given two strings $S$ and $P$, the Episode Matching problem is to find the shortest substring of $S$ that contains $P$ as a subsequence. The best known upper bound for this problem is $\tilde O(nm)$ by Das et al. (1997) , where $n,m$ are…

Data Structures and Algorithms · Computer Science 2024-02-15 Philip Bille , Inge Li Gørtz , Shay Mozes , Teresa Anna Steiner , Oren Weimann

A string $w$ is said to be a minimal unique substring (MUS) of a string $T$ if $w$ occurs exactly once in $T$, and any proper substring of $w$ occurs at least twice in $T$. It is known that the number of MUSs in a string $T$ of length $n$…

Data Structures and Algorithms · Computer Science 2025-08-25 Hiroto Fujimaru , Takuya Mieno , Shunsuke Inenaga

Given $m$ documents of total length $n$, we consider the problem of finding a longest string common to at least $d \geq 2$ of the documents. This problem is known as the \emph{longest common substring (LCS) problem} and has a classic $O(n)$…

Data Structures and Algorithms · Computer Science 2014-07-03 Tomasz Kociumaka , Tatiana Starikovskaya , Hjalte Wedel Vildhøj

Let $\mathcal{D}$ be a collection of $D$ documents, which are strings over an alphabet of size $\sigma$, of total length $n$. We describe a data structure that uses linear space and and reports $k$ most relevant documents that contain a…

Data Structures and Algorithms · Computer Science 2013-08-02 Gonzalo Navarro , Yakov Nekrich

The longest common subsequence (LCS) problem is a central problem in stringology that finds the longest common subsequence of given two strings $A$ and $B$. More recently, a set of four constrained LCS problems (called generalized…

Data Structures and Algorithms · Computer Science 2020-01-17 Kohei Yamada , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

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

The Binary Jumbled String Matching problem is defined as: Given a string $s$ over $\{a,b\}$ of length $n$ and a query $(x,y)$, with $x,y$ non-negative integers, decide whether $s$ has a substring $t$ with exactly $x$ $a$'s and $y$ $b$'s.…

Data Structures and Algorithms · Computer Science 2013-06-03 Golnaz Badkobeh , Gabriele Fici , Steve Kroon , Zsuzsanna Lipták

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

We consider succinct data structures for representing a set of $n$ horizontal line segments in the plane given in rank space to support \emph{segment access}, \emph{segment selection}, and \emph{segment rank} queries. A segment access query…

Data Structures and Algorithms · Computer Science 2024-12-09 Philip Bille , Inge Li Gørtz , Simon R. Tarnow

The suffix trees are fundamental data structures for various kinds of string processing. The suffix tree of a text string $T$ of length $n$ has $O(n)$ nodes and edges, and the string label of each edge is encoded by a pair of positions in…

Data Structures and Algorithms · Computer Science 2023-12-06 Diptarama Hendrian , Takuya Takagi , Shunsuke Inenaga , Keisuke Goto , Mitsuru Funakoshi

Detecting all the strings that occur in a text more frequently or less frequently than expected according to an IID or a Markov model is a basic problem in string mining, yet current algorithms are based on data structures that are either…

Data Structures and Algorithms · Computer Science 2015-08-13 Djamal Belazzougui , Fabio Cunial

A seed in a word is a relaxed version of a period in which the occurrences of the repeating subword may overlap. We show a linear-time algorithm computing a linear-size representation of all the seeds of a word (the number of seeds might be…

Data Structures and Algorithms · Computer Science 2019-03-15 Tomasz Kociumaka , Marcin Kubica , Jakub Radoszewski , Wojciech Rytter , Tomasz Walen

Described are two algorithms to find long approximate palindromes in a string, for example a DNA sequence. A simple algorithm requires O(n)-space and almost always runs in $O(k.n)$-time where n is the length of the string and k is the…

Data Structures and Algorithms · Computer Science 2007-05-23 L. Allison

Deterministic finite automata are one of the simplest and most practical models of computation studied in automata theory. Their conceptual extension is the non-deterministic finite automata which also have plenty of applications. In this…

Data Structures and Algorithms · Computer Science 2019-07-24 Sankardeep Chakraborty , Roberto Grossi , Kunihiko Sadakane , Srinivasa Rao Satti