English
Related papers

Related papers: An Algorithm for the Longest Common Subsequence an…

200 papers

The Longest Common Subsequence (LCS) is a fundamental string similarity measure, and computing the LCS of two strings is a classic algorithms question. A textbook dynamic programming algorithm gives an exact algorithm in quadratic time, and…

Data Structures and Algorithms · Computer Science 2023-02-13 Xiaoyu He , Ray Li

We consider the longest common subsequence problem in the context of subsequences with gap constraints. In particular, following Day et al. 2022, we consider the setting when the distance (i. e., the gap) between two consecutive symbols of…

Data Structures and Algorithms · Computer Science 2023-06-05 Duncan Adamson , Maria Kosche , Tore Koß , Florin Manea , Stefan Siemer

This study develops an algorithm to solve a variation of the Shortest Common Superstring (SCS) problem. There are two modifications to the base SCS problem. First, one string in the set S is allowed to have up to K mistakes, defined as not…

Data Structures and Algorithms · Computer Science 2024-11-05 Arthur Gilfanov

Finding an Approximate Longest Common Substring (ALCS) within a given set $S=\{s_1,s_2,\ldots,s_m\}$ of $m \ge 2$ strings is a key problem in computational biology, such as identifying related mutations across multiple genetic sequences. We…

Data Structures and Algorithms · Computer Science 2025-09-22 Hamed Hasibi , Neerja Mhaskar , W. F. Smyth

Given a string $T$ with length $n$ whose characters are drawn from an ordered alphabet of size $\sigma$, its longest Lyndon subsequence is a longest subsequence of $T$ that is a Lyndon word. We propose algorithms for finding such a…

Data Structures and Algorithms · Computer Science 2022-01-19 Hideo Bannai , Tomohiro I , Tomasz Kociumaka , Dominik Köppl , Simon J. Puglisi

The longest common subsequence (LCS) is a fundamental problem in string processing which has numerous algorithmic studies, extensions, and applications. A sequence $u_1, \ldots, u_f$ of $f$ strings s said to be an ($f$-)segmentation of a…

Data Structures and Algorithms · Computer Science 2025-02-27 Yuki Yonemoto , Takuya Mieno , Shunsuke Inenaga , Ryo Yoshinaka , Ayumi Shinohara

In the longest common substring (LCS) problem, we are given two strings $S$ and $T$, each of length at most $n$, and we are asked to find a longest string occurring as a fragment of both $S$ and $T$. This is a classical and well-studied…

Data Structures and Algorithms · Computer Science 2018-07-17 Amihood Amir , Panagiotis Charalampopoulos , Solon P. Pissis , Jakub Radoszewski

Longest common substring (LCS), longest palindrome substring (LPS), and Ulam distance (UL) are three fundamental string problems that can be classically solved in near linear time. In this work, we present sublinear time quantum algorithms…

Quantum Physics · Physics 2023-12-29 François Le Gall , Saeed Seddighin

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 consider two versions of the Text Assembling problem. We are given a sequence of strings $s^1,\dots,s^n$ of total length $L$ that is a dictionary, and a string $t$ of length $m$ that is texts. The first version of the…

Quantum Physics · Physics 2024-04-05 Kamil Khadiev , Carlos Manuel Bosch Machado , Zeyu Chen , Junde Wu

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

We study sketching and streaming algorithms for the Longest Common Subsequence problem (LCS) on strings of small alphabet size $|\Sigma|$. For the problem of deciding whether the LCS of strings $x,y$ has length at least $L$, we obtain a…

Data Structures and Algorithms · Computer Science 2018-10-03 Karl Bringmann , Bhaskar Ray Chaudhury

The {\em longest common subsequence (LCS)} problem is a classic and well-studied problem in computer science. Palindrome is a word which reads the same forward as it does backward. The {\em longest common palindromic subsequence (LCPS)}…

Data Structures and Algorithms · Computer Science 2011-10-25 Shihabur Rahman Chowdhury , Md. Mahbubul Hasan , Sumaiya Iqbal , M. Sohel Rahman

We study algorithms for solving three problems on strings. The first one is the Most Frequently String Search Problem. The problem is the following. Assume that we have a sequence of $n$ strings of length $k$. The problem is finding the…

Quantum Physics · Physics 2020-01-08 Kamil Khadiev , Artem Ilikaev

The longest common subsequence (LCS) problem is a central problem in stringology that finds the longest common subsequence of given two strings $A$ and $B$. More recently, a set of four constrained LCS problems (called generalized…

Data Structures and Algorithms · Computer Science 2020-01-17 Kohei Yamada , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

The Shortest Common Superstring problem (SCS) consists, for a set of strings S = {s_1,...,s_n}, in finding a minimum length string that contains all s_i, 1<= i <= n, as substrings. While a 2+11/30 approximation ratio algorithm has recently…

Data Structures and Algorithms · Computer Science 2018-05-02 Tristan Braquelaire , Marie Gasparoux , Mathieu Raffinot , Raluca Uricaru

Lately, there is a growing interest in dynamic string matching problems. Specifically, the dynamic Longest Common Factor problem has been researched and some interesting results has been reached. In this paper we examine another classic…

Data Structures and Algorithms · Computer Science 2019-06-25 Amihood Amir , Itai Boneh

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 classic longest common substring (LCS) problem, we are given two strings $S$ and $T$, each of length at most $n$, over an alphabet of size $\sigma$, and we are asked to find a longest string occurring as a fragment of both $S$ and…

Data Structures and Algorithms · Computer Science 2025-11-18 Panagiotis Charalampopoulos , Tomasz Kociumaka , Jakub Radoszewski , Solon P. Pissis

Given a sequence $S$ of length $n$, a letter-duplicated subsequence is a subsequence of $S$ in the form of $x_1^{d_1}x_2^{d_2}\cdots x_k^{d_k}$ with $x_i\in\Sigma$, $x_j\neq x_{j+1}$ and $d_i\geq 2$ for all $i$ in $[k]$ and $j$ in $[k-1]$.…

Data Structures and Algorithms · Computer Science 2022-01-05 Wenfeng Lai , Adiesha Liyanage , Binhai Zhu , Peng Zou