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We present the first $\mathrm{o}(n)$-space polynomial-time algorithm for computing the length of a longest common subsequence. Given two strings of length $n$, the algorithm runs in $\mathrm{O}(n^{3})$ time with $\mathrm{O}\left(\frac{n…

Data Structures and Algorithms · Computer Science 2020-09-21 Masashi Kiyomi , Takashi Horiyama , Yota Otachi

The longest common substring problem consists in finding a longest string that appears as a (contiguous) substring of two input strings. We consider the dynamic variant of this problem, in which we are to maintain two dynamic strings $S$…

Data Structures and Algorithms · Computer Science 2026-04-09 Panagiotis Charalampopoulos , Paweł Gawrychowski , Karol Pokorski

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

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

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 {\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

The Longest Common Subsequence (LCS) problem is a very important problem in math- ematics, which has a broad application in scheduling problems, physics and bioinformatics. It is known that the given two random sequences of infinite…

Discrete Mathematics · Computer Science 2013-06-19 Kang Ning , Kwok Pui Choi

We introduce the Longest Common Circular Factor (LCCF) problem in which, given strings $S$ and $T$ of length $n$, we are to compute the longest factor of $S$ whose cyclic shift occurs as a factor of $T$. It is a new similarity measure, an…

This paper addresses the Restricted Longest Common Subsequence (RLCS) problem, an extension of the well-known Longest Common Subsequence (LCS) problem. This problem has significant applications in bioinformatics, particularly for…

Artificial Intelligence · Computer Science 2024-10-17 Marko Djukanović , Jaume Reixach , Ana Nikolikj , Tome Eftimov , Aleksandar Kartelj , Christian Blum

We present an $O(1)$-round fully-scalable deterministic massively parallel algorithm for computing the min-plus matrix multiplication of unit-Monge matrices. We use this to derive a $O(\log n)$-round fully-scalable massively parallel…

Data Structures and Algorithms · Computer Science 2024-04-23 Jaehyun Koo

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

We consider the general problem of the Longest Common Subsequence (LCS) on weighted sequences. Weighted sequences are an extension of classical strings, where in each position every letter of the alphabet may occur with some probability.…

Computational Complexity · Computer Science 2020-07-21 Evangelos Kipouridis , Kostas Tsichlas

In the classical longest palindromic substring (LPS) problem, we are given a string $S$ of length $n$, and the task is to output a longest palindromic substring in $S$. Gilbert, Hajiaghayi, Saleh, and Seddighin [SPAA 2023] showed how to…

Data Structures and Algorithms · Computer Science 2025-11-18 Solon P. Pissis

This note provides very simple, efficient algorithms for computing the number of distinct longest common subsequences of two input strings and for computing the number of LCS embeddings.

Data Structures and Algorithms · Computer Science 2007-05-23 Ronald I. Greenberg

A longest common extension (LCE) query on a string computes the length of the longest common suffix or prefix at two given positions. A dynamic LCE algorithm maintains a data structure that allows efficient LCE queries on a string that can…

Data Structures and Algorithms · Computer Science 2026-04-15 Daniel Albert

We present an algorithm computing the longest periodic subsequence of a string of length $n$ in $O(n^7)$ time with $O(n^4)$ words of space. We obtain improvements when restricting the exponents or extending the search allowing the reported…

Data Structures and Algorithms · Computer Science 2022-02-16 Hideo Bannai , Tomohiro I , Dominik Köppl

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 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

Longest Increasing Subsequence (LIS) is a fundamental problem in combinatorics and computer science. Previously, there have been numerous works on both upper bounds and lower bounds of the time complexity of computing and approximating LIS,…

Computational Complexity · Computer Science 2023-09-06 Xin Li , Yu Zheng

We study quantum algorithms for several fundamental string problems, including Longest Common Substring, Lexicographically Minimal String Rotation, and Longest Square Substring. These problems have been widely studied in the stringology…

Data Structures and Algorithms · Computer Science 2021-10-22 Shyan Akmal , Ce Jin