English
Related papers

Related papers: Linear-space LCS enumeration with quadratic-time d…

200 papers

Longest Common Subsequence ($LCS$) deals with the problem of measuring similarity of two strings. While this problem has been analyzed for decades, the recent interest stems from a practical observation that considering single characters is…

Data Structures and Algorithms · Computer Science 2018-05-25 Filip Pavetić , Ivan Katanić , Gustav Matula , Goran Žužić , Mile Šikić

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 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

Finding the common subsequences of $L$ multiple strings has many applications in the area of bioinformatics, computational linguistics, and information retrieval. A well-known result states that finding a Longest Common Subsequence (LCS)…

Data Structures and Algorithms · Computer Science 2020-09-09 Jin Cao , Dewei Zhong

In this paper, we consider a generalized longest common subsequence problem with multiple substring exclusion constrains. For the two input sequences $X$ and $Y$ of lengths $n$ and $m$, and a set of $d$ constrains $P=\{P_1,...,P_d\}$ of…

Data Structures and Algorithms · Computer Science 2013-03-11 Lei Wang , Xiaodong Wang , Yingjie Wu , Daxin Zhu

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

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

Two important similarity measures between sequences are the longest common subsequence (LCS) and the dynamic time warping distance (DTWD). The computations of these measures for two given sequences are central tasks in a variety of…

Computational Complexity · Computer Science 2015-02-02 Amir Abboud , Arturs Backurs , Virginia Vassilevska Williams

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

This paper reformulates the problem of finding a longest common increasing subsequence of the two given input sequences in a very succinct way. An extremely simple linear space algorithm based on the new formula can find a longest common…

Data Structures and Algorithms · Computer Science 2016-08-26 Daxin Zhu , Lei Wang , Tinran Wang , Xiaodong Wang

Given two sequences $A[1..n]$ and $B[1..m]$ over a totally ordered alphabet, the \emph{Longest Common Bitonic Subsequence} (LCBS) problem asks for a longest common subsequence that is strictly increasing up to a single peak element and…

Data Structures and Algorithms · Computer Science 2026-01-15 Md. Tanzeem Rahat , Md. Manzurul Hasan

In this paper, we consider a generalized longest common subsequence problem, in which a constraining sequence of length $s$ must be included as a substring and the other constraining sequence of length $t$ must be excluded as a subsequence…

Data Structures and Algorithms · Computer Science 2015-06-02 Daxin Zhu , Lei Wang , Yingjie Wu , Xiaodong Wang

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

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

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

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

The Longest Common Subsequence (LCS) is the problem of finding a subsequence among a set of strings that has two properties of being common to all and is the longest. The LCS has applications in computational biology and text editing, among…

Artificial Intelligence · Computer Science 2023-06-07 Alireza Abdi , Masih Hajsaeedi , Mohsen Hooshmand

Consider two independent random strings having same length and taking values uniformly in a common finite alphabet. We study the order of the variance of the length of the longest common subsequences (LCS) of these strings when long blocks,…

Probability · Mathematics 2016-09-26 S. Amsalu , C. Houdré , H. Matzinger

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 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