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A pattern $\alpha$ is a string of variables and terminal letters. We say that $\alpha$ matches a word $w$, consisting only of terminal letters, if $w$ can be obtained by replacing the variables of $\alpha$ by terminal words. The matching…

Data Structures and Algorithms · Computer Science 2022-07-18 Paweł Gawrychowski , Florin Manea , Stefan Siemer

In this paper we study a variant of string pattern matching which deals with tuples of strings known as \textit{multi-track strings}. Multi-track strings are a generalisation of strings (or \textit{single-track strings}) that have primarily…

Data Structures and Algorithms · Computer Science 2019-12-02 Carl Barton , Ewan Birney , Tomas Fitzgerald

The fundamental question considered in algorithms on strings is that of indexing, that is, preprocessing a given string for specific queries. By now we have a number of efficient solutions for this problem when the queries ask for an exact…

Data Structures and Algorithms · Computer Science 2023-04-04 Paweł Gawrychowski , Garance Gourdel , Tatiana Starikovskaya , Teresa Anna Steiner

String matching is the problem of finding all the occurrences of a pattern in a text. We propose improved versions of the fast family of string matching algorithms based on hashing $q$-grams. The improvement consists of considering minimal…

Data Structures and Algorithms · Computer Science 2023-03-13 Thierry Lecroq

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

A weighted string over an alphabet of size $\sigma$ is a string in which a set of letters may occur at each position with respective occurrence probabilities. Weighted strings, also known as position weight matrices or uncertain sequences,…

Data Structures and Algorithms · Computer Science 2015-12-09 Carl Barton , Chang Liu , Solon P. Pissis

This paper focuses on pattern matching in the DNA sequence. It was inspired by a previously reported method that proposes encoding both pattern and sequence using prime numbers. Although fast, the method is limited to rather small pattern…

Computer Vision and Pattern Recognition · Computer Science 2016-11-21 Janja Paliska Soldo , Ana Sovic Krzic , and Damir Sersic

In this work, we consider the problem of pattern matching under the dynamic time warping (DTW) distance motivated by potential applications in the analysis of biological data produced by the third generation sequencing. To measure the DTW…

Data Structures and Algorithms · Computer Science 2022-09-01 Garance Gourdel , Anne Driemel , Pierre Peterlongo , Tatiana Starikovskaya

Given a text $T$ of length $n$ and a pattern $P$ of length $m$, the string matching problem is a task to find all occurrences of $P$ in $T$. In this study, we propose an algorithm that solves this problem in $O((n + m)q)$ time considering…

Data Structures and Algorithms · Computer Science 2020-04-14 Satoshi Kobayashi , Diptarama Hendrian , Ryo Yoshinaka , Ayumi Shinohara

Given a log and a specification, timed pattern matching aims at exhibiting for which start and end dates a specification holds on that log. For example, "a given action is always followed by another action before a given deadline". This…

Formal Languages and Automata Theory · Computer Science 2024-07-26 Masaki Waga , Étienne André , Ichiro Hasuo

We consider the classical exact multiple string matching problem. Our solution is based on $q$-grams combined with pattern superimposition, bit-parallelism and alphabet size reduction. We discuss the pros and cons of the various…

Data Structures and Algorithms · Computer Science 2021-12-07 Robert Susik , Szymon Grabowski , Kimmo Fredriksson

This paper addresses the online exact string matching problem which consists in finding all occurrences of a given pattern p in a text t. It is an extensively studied problem in computer science, mainly due to its direct applications to…

Data Structures and Algorithms · Computer Science 2010-12-14 Simone Faro , Thierry Lecroq

We propose a new indexing structure for parameterized strings, called parameterized position heap. Parameterized position heap is applicable for parameterized pattern matching problem, where the pattern matches a substring of the text if…

Data Structures and Algorithms · Computer Science 2017-04-19 Diptarama , Takashi Katsura , Yuhei Otomo , Kazuyuki Narisawa , Ayumi Shinohara

A natural probabilistic model for motif discovery has been used to experimentally test the quality of motif discovery programs. In this model, there are $k$ background sequences, and each character in a background sequence is a random…

Data Structures and Algorithms · Computer Science 2012-03-14 Bin Fu , Yunhui Fu

We study the design of efficient algorithms for combinatorial pattern matching. More concretely, we study algorithms for tree matching, string matching, and string matching in compressed texts.

Data Structures and Algorithms · Computer Science 2007-09-03 Philip Bille

String matching is the problem of deciding whether a given $n$-bit string contains a given $k$-bit pattern. We study the complexity of this problem in three settings. Communication complexity. For small $k$, we provide near-optimal upper…

Computational Complexity · Computer Science 2019-02-21 Alexander Golovnev , Mika Göös , Daniel Reichman , Igor Shinkar

Term pattern matching is the problem of finding all pattern matches in a subject term, given a set of patterns. Finding efficient algorithms for this problem is an important direction for research [19]. We present a new set automaton…

Formal Languages and Automata Theory · Computer Science 2021-06-30 Rick Erkens , Jan Friso Groote

Pattern matching is a powerful tool which is part of many functional programming languages as well as computer algebra systems such as Mathematica. Among the existing systems, Mathematica offers the most expressive pattern matching.…

Symbolic Computation · Computer Science 2017-05-03 Manuel Krebber

Finding repeated patterns or motifs in a time series is an important unsupervised task that has still a number of open issues, starting by the definition of motif. In this paper, we revise the notion of motif support, characterizing it as…

Machine Learning · Computer Science 2016-12-06 Joan Serrà , Aleksandar Matic , Josep Luis Arcos , Alexandros Karatzoglou

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