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The text-to-pattern Hamming distances problem asks to compute the Hamming distances between a given pattern of length $m$ and all length-$m$ substrings of a given text of length $n\ge m$. We focus on the $k$-mismatch version of the problem,…

Data Structures and Algorithms · Computer Science 2022-03-30 Raphaël Clifford , Paweł Gawrychowski , Tomasz Kociumaka , Daniel P. Martin , Przemysław Uznański

In the $k$-mismatch problem we are given a pattern of length $n$ and a text and must find all locations where the Hamming distance between the pattern and the text is at most $k$. A series of recent breakthroughs have resulted in an…

Data Structures and Algorithms · Computer Science 2021-06-22 Paweł Gawrychowski , Tatiana Starikovskaya

The $k$-mappability problem has two integers parameters $m$ and $k$. For every subword of size $m$ in a text $S$, we wish to report the number of indices in $S$ in which the word occurs with at most $k$ mismatches. The problem was lately…

Data Structures and Algorithms · Computer Science 2021-06-15 Amihood Amir , Itai Boneh , Eitan Kondratovsky

We revisit a fundamental problem in string matching: given a pattern of length m and a text of length n, both over an alphabet of size $\sigma$, compute the Hamming distance between the pattern and the text at every location. Several…

Data Structures and Algorithms · Computer Science 2020-01-03 Timothy M. Chan , Shay Golan , Tomasz Kociumaka , Tsvi Kopelowitz , Ely Porat

We consider the problem of finding, given two documents of total length $n$, a longest string occurring as a substring of both documents. This problem, known as the Longest Common Substring (LCS) problem, has a classic $O(n)$-time solution…

Data Structures and Algorithms · Computer Science 2020-04-29 Stav Ben-Nun , Shay Golan , Tomasz Kociumaka , Matan Kraus

This paper investigates the approximability of the Longest Common Subsequence (LCS) problem. The fastest algorithm for solving the LCS problem exactly runs in essentially quadratic time in the length of the input, and it is known that under…

Data Structures and Algorithms · Computer Science 2021-05-10 Shyan Akmal , Virginia Vassilevska Williams

In this paper, we revisit the much studied LCS problem for two given sequences. Based on the algorithm of Iliopoulos and Rahman for solving the LCS problem, we have suggested 3 new improved algorithms. We first reformulate the problem in a…

Data Structures and Algorithms · Computer Science 2015-08-25 Daxin Zhu , Lei Wang , Yingjie Wu , Xiaodong Wang

In the longest common substring problem, we are given two strings of length $n$ and must find a substring of maximal length that occurs in both strings. It is well known that the problem can be solved in linear time, but the solution is not…

Data Structures and Algorithms · Computer Science 2018-08-21 Tomasz Kociumaka , Jakub Radoszewski , Tatiana Starikovskaya

In the problem of the longest common substring with $k$ mismatches we are given two strings $X, Y$ and must find the maximal length $\ell$ such that there is a length-$\ell$ substring of $X$ and a length-$\ell$ substring of $Y$ that differ…

Data Structures and Algorithms · Computer Science 2020-04-29 Garance Gourdel , Tomasz Kociumaka , Jakub Radoszewski , Tatiana Starikovskaya

A border of a string is a non-empty proper prefix of the string that is also a suffix. A string is unbordered if it has no border. The longest unbordered factor is a fundamental notion in stringology, closely related to string periodicity.…

Data Structures and Algorithms · Computer Science 2025-07-23 Shoma Sekizaki , Takuya Mieno

In this paper we introduce a new family of string processing problems. We are given two or more strings and we are asked to compute a factor common to all strings that preserves a specific property and has maximal length. Here we consider…

Data Structures and Algorithms · Computer Science 2018-10-05 Lorraine A. K Ayad , Giulia Bernardini , Roberto Grossi , Costas S. Iliopoulos , Nadia Pisanti , Solon P. Pissis , Giovanna Rosone

Longest Common Substring (LCS) is an important text processing problem, which has recently been investigated in the quantum query model. The decisional version of this problem, LCS with threshold $d$, asks whether two length-$n$ input…

Data Structures and Algorithms · Computer Science 2022-11-30 Ce Jin , Jakob Nogler

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 consider the classic problem of computing the Longest Common Subsequence (LCS) of two strings of length $n$. While a simple quadratic algorithm has been known for the problem for more than 40 years, no faster algorithm has been found…

Data Structures and Algorithms · Computer Science 2021-06-16 Karl Bringmann , Vincent Cohen-Addad , Debarati Das

Palindromes are strings that read the same forward and backward. Problems of computing palindromic structures in strings have been studied for many years with a motivation of their application to biology. The longest palindrome problem is…

Data Structures and Algorithms · Computer Science 2023-06-21 Kazuki Mitani , Takuya Mieno , Kazuhisa Seto , Takashi Horiyama

We present a practical algorithm for the cyclic longest common subsequence (CLCS) problem that runs in O(mn) time, where m and n are the lengths of the two input strings. While this is not necessarily an asymptotic improvement over the…

Data Structures and Algorithms · Computer Science 2012-08-17 Andy Nguyen

Abelian string matching problems are becoming an object of considerable interest in last years. Very recently, Alatabbi et al. \cite{AILR2015} presented the first solution for the longest common Abelian factor problem for a pair of strings,…

Data Structures and Algorithms · Computer Science 2015-03-12 Szymon Grabowski

Given a string $s$ of length $n$ over a general alphabet and an integer $k$, the problem is to decide whether $s$ is a concatenation of $k$ nonempty palindromes. Two previously known solutions for this problem work in time $O(kn)$ and…

Data Structures and Algorithms · Computer Science 2020-07-07 Mikhail Rubinchik , Arseny M. Shur

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

Approximate string matching is the problem of finding all factors of a text t of length n that are at a distance at most k from a pattern x of length m. Approximate circular string matching is the problem of finding all factors of t that…

Data Structures and Algorithms · Computer Science 2016-04-26 Carl Barton , Costas S. Iliopoulos , Solon P. Pissis