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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

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

We propose a quantum algorithm for closest pattern matching which allows us to search for as many distinct patterns as we wish in a given string (database), requiring a query function per symbol of the pattern alphabet. This represents a…

Quantum Physics · Physics 2007-05-23 P. Mateus , Y. Omar

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. In the last two…

Information Retrieval · Computer Science 2012-10-01 Simone Faro , M. Oguzhan Külekci

The problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants…

Data Structures and Algorithms · Computer Science 2008-07-29 Dimitris Papamichail , Georgios Papamichail

In his 1987 paper entitled "Generalized String Matching", Abrahamson introduced {\em pattern matching with character classes} and provided the first efficient algorithm to solve it. The best known solution to date is due to Linhart and…

Data Structures and Algorithms · Computer Science 2021-01-01 Alberto Apostolico , Péter L. Erdős , István Miklós , Johannes Siemons

We introduce a new string matching problem called order-preserving matching on numeric strings where a pattern matches a text if the text contains a substring whose relative orders coincide with those of the pattern. Order-preserving…

Data Structures and Algorithms · Computer Science 2013-02-19 Jinil Kim , Peter Eades , Rudolf Fleischer , Seok-Hee Hong , Costas S. Iliopoulos , Kunsoo Park , Simon J. Puglisi , Takeshi Tokuyama

In the paper, we investigate two problems on strings. The first one is the String matching problem, and the second one is the String comparing problem. We provide a quantum algorithm for the String matching problem that uses exponentially…

Quantum Physics · Physics 2023-05-19 Farid Ablayev , Marat Ablayev , Kamil Khadiev , Nailya Salihova , Alexander Vasiliev

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

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

The timed pattern matching problem is formulated by Ulus et al. and has been actively studied since, with its evident application in monitoring real-time systems. The problem takes as input a timed word/signal and a timed pattern (specified…

Formal Languages and Automata Theory · Computer Science 2018-10-22 Masaki Waga , Takumi Akazaki , Ichiro Hasuo

In this paper we consider several variants of the pattern matching problem. In particular, we investigate the following problems: 1) Pattern matching with k mismatches; 2) Approximate counting of mismatches; and 3) Pattern matching with…

Data Structures and Algorithms · Computer Science 2013-07-05 Marius Nicolae , Sanguthevar Rajasekaran

String matching is a fundamental problem in computer science, with critical applications in text retrieval, bioinformatics, and data analysis. Among the numerous solutions that have emerged for this problem in recent decades,…

Data Structures and Algorithms · Computer Science 2025-03-10 Simone Faro , Arianna Pavone , Caterina Viola

In this paper, we revisit the much studied problem of Pattern Matching with Swaps (Swap Matching problem, for short). We first present a graph-theoretic model, which opens a new and so far unexplored avenue to solve the problem. Then, using…

Data Structures and Algorithms · Computer Science 2013-09-19 Pritom Ahmed , Costas S. Iliopoulos , A. S. M. Sohidull Islam , M. Sohel Rahman

This study aims to publish a novel similarity metric to increase the speed of comparison operations. Also the new metric is suitable for distance-based operations among strings. Most of the simple calculation methods, such as string length…

Data Structures and Algorithms · Computer Science 2014-01-28 Sadi Evren Seker , Oguz Altun , Uğur Ayan , Cihan Mert

More than 120 algorithms have been developed for exact string matching within the last 40 years. We show by experiments that the \naive{} algorithm exploiting SIMD instructions of modern CPUs (with symbols compared in a special order) is…

Data Structures and Algorithms · Computer Science 2016-12-06 Jorma Tarhio , Jan Holub , Emanuele Giaquinta

We study the classical approximate string matching problem, that is, given strings $P$ and $Q$ and an error threshold $k$, find all ending positions of substrings of $Q$ whose edit distance to $P$ is at most $k$. Let $P$ and $Q$ have…

Data Structures and Algorithms · Computer Science 2011-03-21 Philip Bille

In this work, we tackle a natural variation of the String Matching Problem on the case of a dynamic pattern, that is, given a static text $T$ and a pattern $P$, we want to support character additions and deletions to the pattern, and after…

Data Structures and Algorithms · Computer Science 2025-06-16 Bruno Monteiro , Vinicius dos Santos

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

We introduce a novel definition of approximate palindromes in strings, and provide an algorithm to find all maximal approximate palindromes in a string with up to $k$ errors. Our definition is based on the usual edit operations of…

Data Structures and Algorithms · Computer Science 2007-05-23 A. H. L. Porto , V. C. Barbosa