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We consider the longest common subsequence (LCS) problem with the restriction that the common subsequence is required to consist of at least $k$ length substrings. First, we show an $O(mn)$ time algorithm for the problem which gives a…

Data Structures and Algorithms · Computer Science 2017-02-07 Yohei Ueki , Diptarama , Masatoshi Kurihara , Yoshiaki Matsuoka , Kazuyuki Narisawa , Ryo Yoshinaka , Hideo Bannai , Shunsuke Inenaga , Ayumi Shinohara

The Longest Common Subsequence (LCS) of two strings is a fundamental string similarity measure with a classical dynamic programming solution taking quadratic time. Despite significant efforts, little progress was made in improving the…

Data Structures and Algorithms · Computer Science 2021-12-17 Negev Shekel Nosatzki

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

The Longest Common Subsequence (LCS) problem is a fundamental problem of sequence comparison. A natural approximation to this problem is a model in which every pairs of letters of two ``sequences'' are matched independently of the other…

Disordered Systems and Neural Networks · Physics 2016-08-31 J. Boutet de Monvel

Given a set of $k$ strings $I$, their longest common subsequence (LCS) is the string with the maximum length that is a subset of all the strings in $I$. A data-structure for this problem preprocesses $I$ into a data-structure such that the…

Data Structures and Algorithms · Computer Science 2021-01-13 Sepideh Aghamolaei

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 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

One of the most fundamental method for comparing two given strings $A$ and $B$ is the longest common subsequence (LCS), where the task is to find (the length) of an LCS of $A$ and $B$. In this paper, we deal with the STR-IC-LCS problem…

Data Structures and Algorithms · Computer Science 2024-05-21 Yuki Yonemoto , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai

The Shortest Superstring Problem (SSP) consists, for a set of strings S = {s_1,...,s_n}, to find a minimum length string that contains all s_i, 1 <= i <= k, as substrings. This problem is proved to be NP-Complete and APX-hard. Guaranteed…

Discrete Mathematics · Computer Science 2016-05-19 Tristan Braquelaire , Marie Gasparoux , Mathieu Raffinot , Raluca Uricaru

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

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

The Longest Common Subsequence Problem (LCS) deals with finding the longest subsequence among a given set of strings. The LCS problem is an NP-hard problem which makes it a target for lots of effort to find a better solution with heuristics…

Data Structures and Algorithms · Computer Science 2022-06-24 Alireza Abdi , Mohsen Hooshmand

Motivated by computing duplication patterns in sequences, a new fundamental problem called the longest subsequence-repeated subsequence (LSRS) is proposed. Given a sequence $S$ of length $n$, a letter-repeated subsequence is a subsequence…

Data Structures and Algorithms · Computer Science 2023-09-01 Manuel Lafond , Wenfeng Lai , Adiesha Liyanage , Binhai Zhu

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

We study a variation of the classical Shortest Common Superstring (SCS) problem in which a shortest superstring of a finite set of strings $S$ is sought containing as a factor every string of $S$ or its reversal. We call this problem…

Data Structures and Algorithms · Computer Science 2015-12-08 Gabriele Fici , Tomasz Kociumaka , Jakub Radoszewski , Wojciech Rytter , Tomasz Waleń

In the Shortest Common Superstring (SCS) problem, one is given a collection of strings, and needs to find a shortest string containing each of them as a substring. SCS admits $2\frac{11}{23}$-approximation in polynomial time (Mucha,…

Data Structures and Algorithms · Computer Science 2020-06-05 Alexander Golovnev , Alexander S. Kulikov , Alexander Logunov , Ivan Mihajlin , Maksim Nikolaev

Let $\Sigma$ be an alphabet. For two strings $X$, $Y$, and a constrained string $P$ over the alphabet $\Sigma$, the constrained longest common subsequence and substring problem for two strings $X$ and $Y$ with respect to $P$ is to find a…

Data Structures and Algorithms · Computer Science 2023-08-04 R. Li , J. Deka , K. Deka , D. Li

A classical measure of string comparison is given by the longest common subsequence (LCS) problem on a pair of strings. We consider its generalisation, called the semi-local LCS problem, which arises naturally in many string-related…

Data Structures and Algorithms · Computer Science 2015-03-13 Alexander Tiskin

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

The 2-LCPS problem, first introduced by Chowdhury et al. [Fundam. Inform., 129(4):329-340, 2014], asks one to compute (the length of) a longest palindromic common subsequence between two given strings $A$ and $B$. We show that the 2-LCPS…

Data Structures and Algorithms · Computer Science 2016-12-23 Shunsuke Inenaga , Heikki Hyyrö