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We consider string matching with variable length gaps. Given a string $T$ and a pattern $P$ consisting of strings separated by variable length gaps (arbitrary strings of length in a specified range), the problem is to find all ending…

Data Structures and Algorithms · Computer Science 2011-10-14 Philip Bille , Inge Li Goertz , Hjalte Wedel Vildhøj , David Kofoed Wind

We study pattern matching problems on two major representations of uncertain sequences used in molecular biology: weighted sequences (also known as position weight matrices, PWM) and profiles (i.e., scoring matrices). In the simple version,…

Data Structures and Algorithms · Computer Science 2016-07-12 Tomasz Kociumaka , Solon P. Pissis , Jakub Radoszewski

Searching for all occurrences of a pattern in a text is a fundamental problem in computer science with applications in many other fields, like natural language processing, information retrieval and computational biology. Sampled string…

Data Structures and Algorithms · Computer Science 2019-08-19 Simone Faro , Arianna Pavone , Francesco Pio Marino

Online string matching is a computational problem involving the search for patterns or substrings in a large text dataset, with the pattern and text being processed sequentially, without prior access to the entire text. Its relevance stems…

Data Structures and Algorithms · Computer Science 2023-10-25 Matthew N. Palmer , Simone Faro , Stefano Scafiti

Given a set of pattern strings $\mathcal{P}=\{P_1, P_2,\ldots P_k\}$ and a text string $S$, the classic dictionary matching problem is to report all occurrences of each pattern in $S$. We study the dictionary problem in the compressed…

Data Structures and Algorithms · Computer Science 2025-09-04 Philip Bille , Inge Li Gørtz , Simon J. Puglisi , Simon R. Tarnow

Pattern matching is a fundamental process in almost every scientific domain. The problem involves finding the positions of a given pattern (usually of short length) in a reference stream of data (usually of large length). The matching can…

Data Structures and Algorithms · Computer Science 2022-07-01 Anas Al-okaily , Abdelghani Tbakhi

We present new algorithms for the problem of multiple string matching of gapped patterns, where a gapped pattern is a sequence of strings such that there is a gap of fixed length between each two consecutive strings. The problem has…

Data Structures and Algorithms · Computer Science 2014-07-08 Emanuele Giaquinta , Kimmo Fredriksson , Szymon Grabowski , Alexandru I. Tomescu , Esko Ukkonen

Motivated by the imminent growth of massive, highly redundant genomic databases, we study the problem of compressing a string database while simultaneously supporting fast random access, substring extraction and pattern matching to the…

Data Structures and Algorithms · Computer Science 2012-11-01 Travis Gagie , Paweł Gawrychowski , Christopher Hoobin , Simon J. Puglisi

Two strings are considered to have parameterized matching when there exists a bijection of the parameterized alphabet onto itself such that it transforms one string to another. Parameterized matching has application in software duplication…

Data Structures and Algorithms · Computer Science 2024-12-03 Apurba Saha , Iftekhar Hakim Kaowsar , Mahdi Hasnat Siyam , M. Sohel Rahman

We study here the so called subsequence pattern matching also known as hidden pattern matching in which one searches for a given pattern $w$ of length $m$ as a subsequence in a random text of length $n$. The quantity of interest is the…

Probability · Mathematics 2020-03-24 Svante Janson , Wojciech Szpankowski

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

Approximate pattern matching is a natural and well-studied problem on strings: Given a text $T$, a pattern $P$, and a threshold $k$, find (the starting positions of) all substrings of $T$ that are at distance at most $k$ from $P$. We…

Data Structures and Algorithms · Computer Science 2020-11-17 Panagiotis Charalampopoulos , Tomasz Kociumaka , Philip Wellnitz

In this paper we investigate the \emph{approximate string matching problem} when the allowed edit operations are \emph{non-overlapping unbalanced translocations of adjacent factors}. Such kind of edit operations take place when two adjacent…

Data Structures and Algorithms · Computer Science 2021-01-05 Domenico Cantone , Simone Faro , Arianna Pavone

Given a pattern x of length m and a text y of length n, both over an ordered alphabet, the order-preserving pattern matching problem consists in finding all substrings of the text with the same relative order as the pattern. It is an…

Data Structures and Algorithms · Computer Science 2015-01-19 Simone Faro , Oğuzhan Külekci

Cartesian tree pattern matching consists of finding all the factors of a text that have the same Cartesian tree than a given pattern. There already exist theoretical and practical solutions for the exact case. In this paper, we propose the…

Data Structures and Algorithms · Computer Science 2025-05-15 Bastien Auvray , Julien David , Samah Ghazawi , Richard Groult , Gad M. Landau , Thierry Lecroq

We consider document listing on string collections, that is, finding in which strings a given pattern appears. In particular, we focus on repetitive collections: a collection of size $N$ over alphabet $[1,\sigma]$ is composed of $D$ copies…

Data Structures and Algorithms · Computer Science 2018-11-15 Gonzalo Navarro

The binary string matching problem consists in finding all the occurrences of a pattern in a text where both strings are built on a binary alphabet. This is an interesting problem in computer science, since binary data are omnipresent in…

Data Structures and Algorithms · Computer Science 2008-10-15 Simone Faro , Thierry Lecroq

The classical pattern matching asks for locating all occurrences of one string, called the pattern, in another, called the text, where a string is simply a sequence of characters. Due to the potential practical applications, it is desirable…

Data Structures and Algorithms · Computer Science 2024-10-30 Jonas Ellert , Paweł Gawrychowski , Adam Górkiewicz , Tatiana Starikovskaya

In this paper, we extend the notion of gapped strings to elastic-degenerate strings. An elastic-degenerate string can been seen as an ordered collection of k > 1 seeds (substrings/subpatterns) interleaved by elastic-degenerate symbols such…

Data Structures and Algorithms · Computer Science 2016-10-27 Costas Iliopoulos , Ritu Kundu , Solon Pissis

We consider the Consensus Patterns problem, where, given a set of input strings, one is asked to extract a long-enough pattern which appears (with some errors) in all strings. We prove that this problem is W[1]-hard when parameterized by…

Computational Complexity · Computer Science 2017-02-28 Laurent Bulteau