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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

In this work, we consider a variant of the classical Longest Common Subsequence problem called Doubly-Constrained Longest Common Subsequence (DC-LCS). Given two strings s1 and s2 over an alphabet A, a set C_s of strings, and a function Co…

Data Structures and Algorithms · Computer Science 2013-11-20 Paola Bonizzoni , Gianluca Della Vedova , Riccardo Dondi , Yuri Pirola

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

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

Longest common subsequence (LCS) is one of the most fundamental problems in combinatorial optimization. Apart from theoretical importance, LCS has enormous applications in bioinformatics, revision control systems, and data comparison…

Data Structures and Algorithms · Computer Science 2020-03-17 MohammadTaghi Hajiaghayi , Masoud Seddighin , Saeed Seddighin , Xiaorui Sun

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 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

We establish an equivalence between two important random ensembles of linear codes: random linear codes (RLCs) and random Reed-Solomon (RS) codes. Specifically, we show that these models exhibit identical behavior with respect to key…

Information Theory · Computer Science 2025-11-17 Matan Levi , Jonathan Mosheiff , Nikhil Shagrithaya

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

We investigate the longest common substring problem for encoded sequences and its asymptotic behaviour. The main result is a strong law of large numbers for a re-scaled version of this quantity, which presents an explicit relation with the…

Probability · Mathematics 2019-12-12 Adriana Coutinho , Rodrigo Lambert , Jérôme Rousseau

Let $X=(X_i)_{i\ge 1}$ and $Y=(Y_i)_{i\ge 1}$ be two sequences of independent and identically distributed (iid) random variables taking their values, uniformly, in a common totally ordered finite alphabet. Let LCI$_n$ be the length of the…

Probability · Mathematics 2018-08-27 Jean-Christophe Breton , Christian Houdré

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

We consider the canonical generalization of the well-studied Longest Increasing Subsequence problem to multiple sequences, called $k$-LCIS: Given $k$ integer sequences $X_1,\dots,X_k$ of length at most $n$, the task is to determine the…

Computational Complexity · Computer Science 2020-04-10 Lech Duraj , Marvin Künnemann , Adam Polak

In this paper, we study for the first time the Diverse Longest Common Subsequences (LCSs) problem under Hamming distance. Given a set of a constant number of input strings, the problem asks to decide if there exists some subset $\mathcal X$…

Data Structures and Algorithms · Computer Science 2024-06-12 Yuto Shida , Giulia Punzi , Yasuaki Kobayashi , Takeaki Uno , Hiroki Arimura

In this paper, we examine the asymptotic behavior of the longest increasing subsequence (LIS) in a uniformly random permutation of $n$ elements. We rely on the Robinson--Schensted--Knuth correspondence, Young tableaux, and key classical…

History and Overview · Mathematics 2025-11-04 Mihir Gupta

For a set of mulitple sequences, their patterns,Longest Common Subsequences (LCS) and Shortest Common Supersequences (SCS) represent different aspects of these sequences profile, and they can all be used for biological sequence comparisons…

Data Structures and Algorithms · Computer Science 2016-11-17 Kang Ning , Hoong Kee Ng , Hon Wai Leong

This paper performs the analysis necessary to bound the running time of known, efficient algorithms for generating all longest common subsequences. That is, we bound the running time as a function of input size for algorithms with time…

Discrete Mathematics · Computer Science 2007-05-23 Ronald I. Greenberg

The problem of the order of the fluctuation of the Longest Common Subsequence (LCS) of two independent sequences has been open for decades. There exist contradicting conjectures on the topic, due to Chvatal - Sankoff in 1975 and Waterman in…

Probability · Mathematics 2010-11-15 Heinrich Matzinger , Felipe Torres

We consider the length L of the longest common subsequence of two randomly uniformly and independently chosen n character words over a k-ary alphabet. Subadditivity arguments yield that the expected value of L, when normalized by n,…

Combinatorics · Mathematics 2007-05-23 Marcos Kiwi , Martin Loebl , Jiri Matousek

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