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The Longest Common Substring (LCS) and Longest Palindromic Substring (LPS) are classical problems in computer science, representing fundamental challenges in string processing. Both problems can be solved in linear time using a classical…

Data Structures and Algorithms · Computer Science 2023-09-06 Domenico Cantone , Simone Faro , Arianna Pavone , Caterina Viola

Given two strings $T$ and $S$ and a set of strings $P$, for each string $p \in P$, consider the unique substrings of $T$ that have $p$ as their prefix and $S$ as their suffix. Two problems then come to mind; the first problem being the…

Data Structures and Algorithms · Computer Science 2022-04-19 Laurentius Leonard , Ken Tanaka

A longest repeat query on a string, motivated by its applications in many subfields including computational biology, asks for the longest repetitive substring(s) covering a particular string position (point query). In this paper, we extend…

Data Structures and Algorithms · Computer Science 2015-11-10 Bojian Xu

In the Longest Common Factor with $k$ Mismatches (LCF$_k$) problem, we are given two strings $X$ and $Y$ of total length $n$, and we are asked to find a pair of maximal-length factors, one of $X$ and the other of $Y$, such that their…

We revisit the classic combinatorial pattern matching problem of finding a longest common subsequence (LCS). For strings $x$ and $y$ of length $n$, a textbook algorithm solves LCS in time $O(n^2)$, but although much effort has been spent,…

Computational Complexity · Computer Science 2018-03-05 Karl Bringmann , Marvin Künnemann

Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in $O(n \log n)$ time and space. Our goal in this paper is to reduce the space consumption while…

Data Structures and Algorithms · Computer Science 2017-12-27 Masashi Kiyomi , Hirotaka Ono , Yota Otachi , Pascal Schweitzer , Jun Tarui

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

We revisit the problem of longest common property preserving substring queries introduced by~Ayad et al. (SPIRE 2018, arXiv 2018). We consider a generalized and unified on-line setting, where we are given a set $X$ of $k$ strings of total…

Data Structures and Algorithms · Computer Science 2019-06-14 Kazuki Kai , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda , Tomasz Kociumaka

The regular expression matching problem asks whether a given regular expression of length $m$ matches a given string of length $n$. As is well known, the problem can be solved in $O(nm)$ time using Thompson's algorithm. Moreover, recent…

Computational Complexity · Computer Science 2026-04-03 Taisei Nogami , Yoshiki Nakamura , Tachio Terauchi

The recently introduced longest common substring with $k$-mismatches ($k$-LCF) problem is to find, given two sequences $S_1$ and $S_2$ of length $n$ each, a longest substring $A_1$ of $S_1$ and $A_2$ of $S_2$ such that the Hamming distance…

Data Structures and Algorithms · Computer Science 2014-10-15 Szymon Grabowski

We revisit the problem of finding shortest unique substring (SUS) proposed recently by [6]. We propose an optimal $O(n)$ time and space algorithm that can find an SUS for every location of a string of size $n$. Our algorithm significantly…

Data Structures and Algorithms · Computer Science 2014-01-14 Atalay Mert İleri , M. Oğuzhan Külekci , Bojian Xu

The Longest Common Subsequence (LCS) Problem asks for the longest sequence of (non-contiguous) matches between two given strings of characters. Using extensive Monte Carlo simulations, we find a finite size scaling law of the form E(L)/N =C…

Disordered Systems and Neural Networks · Physics 2009-10-31 J. Boutet de Monvel

In this paper, we consider a generalized longest common subsequence problem, the string-excluding constrained LCS problem. For the two input sequences $X$ and $Y$ of lengths $n$ and $m$, and a constraint string $P$ of length $r$, the…

Data Structures and Algorithms · Computer Science 2013-01-31 Lei Wang , Xiaodong Wang , Yingjie Wu , Daxin Zhu

Finding the longest common subsequence in $k$-length substrings (LCS$k$) is a recently proposed problem motivated by computational biology. This is a generalization of the well-known LCS problem in which matching symbols from two sequences…

Data Structures and Algorithms · Computer Science 2013-11-20 Sebastian Deorowicz , Szymon Grabowski

The {\em longest common subsequence (LCS)} problem is a classic and well-studied problem in computer science. LCS is a central problem in stringology and finds broad applications in text compression, error-detecting codes and biological…

Data Structures and Algorithms · Computer Science 2010-04-20 Shihabur Rahman Chowdhury , Masud Hasan , Sumaiya Iqbal , M. Sohel Rahman

We describe how, given a text $T [1..n]$ and a positive constant $\epsilon$, we can build a simple $O (z \log n)$-space index, where $z$ is the number of phrases in the LZ77 parse of $T$, such that later, given a pattern $P [1..m]$, in $O…

Data Structures and Algorithms · Computer Science 2022-12-06 Nick Fagan , Jorge Hermo González , Travis Gagie

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

We consider the Abelian longest common factor problem in two scenarios: when input strings are uncompressed and are of size $n$, and when the input strings are run-length encoded and their compressed representations have size at most $m$.…

Data Structures and Algorithms · Computer Science 2018-04-19 Szymon Grabowski , Tomasz Kociumaka , Jakub Radoszewski

The constrained LCS problem asks one to find a longest common subsequence of two input strings $A$ and $B$ with some constraints. The STR-IC-LCS problem is a variant of the constrained LCS problem, where the solution must include a given…

Data Structures and Algorithms · Computer Science 2017-03-16 Keita Kuboi , Yuta Fujishige , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

The problem of finding the longest common subsequence (LCS) for a set of sequences is a very interesting and challenging problem in computer science. This problem is NP-complete, but because of its importance, many heuristic algorithms have…

Data Structures and Algorithms · Computer Science 2009-06-30 Kang Ning