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Longest common subsequence ($\mathsf{LCS}$) is a classic and central problem in combinatorial optimization. While $\mathsf{LCS}$ admits a quadratic time solution, recent evidence suggests that solving the problem may be impossible in truly…

Data Structures and Algorithms · Computer Science 2021-11-23 Aviad Rubinstein , Saeed Seddighin , Zhao Song , Xiaorui Sun

We consider the classic problem of computing the Longest Common Subsequence (LCS) of two strings of length $n$. While a simple quadratic algorithm has been known for the problem for more than 40 years, no faster algorithm has been found…

Data Structures and Algorithms · Computer Science 2021-06-16 Karl Bringmann , Vincent Cohen-Addad , Debarati Das

In this note, we first introduce a new problem called the longest common subsequence and substring problem. Let $X$ and $Y$ be two strings over an alphabet $\Sigma$. The longest common subsequence and substring problem for $X$ and $Y$ is to…

Data Structures and Algorithms · Computer Science 2023-08-03 R. Li , J. Deka , K. Deka

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

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

At CPM 2017, Castelli et al. define and study a new variant of the Longest Common Subsequence Problem, termed the Longest Filled Common Subsequence Problem (LFCS). For the LFCS problem, the input consists of two strings $A$ and $B$ and a…

Data Structures and Algorithms · Computer Science 2019-08-06 Radu Stefan Mincu , Alexandru Popa

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

The Shortest Common Superstring (SCS) problem is a fundamental task in sequence analysis. In genome assembly, however, the double-stranded nature of DNA implies that each fragment may occur either in its original orientation or as its…

Data Structures and Algorithms · Computer Science 2026-03-30 Ryosuke Yamano , Tetsuo Shibuya

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

We present novel randomized approximation schemes for the Edit Distance (ED) problem and the Longest Common Subsequence (LCS) problem that, for any constant $\epsilon>0$, compute a $(1+\epsilon)$-approximation for ED and a…

Data Structures and Algorithms · Computer Science 2026-04-01 Xiao Mao , Aviad Rubinstein

The problem of finding a center string that is `close' to every given string arises and has many applications in computational biology and coding theory. This problem has two versions: the Closest String problem and the Closest Substring…

Computational Engineering, Finance, and Science · Computer Science 2007-05-23 Ming Li , Bin Ma , Lusheng Wang

In this paper we present $LCSk$++: a new metric for measuring the similarity of long strings, and provide an algorithm for its efficient computation. With ever increasing size of strings occuring in practice, e.g. large genomes of plants…

Data Structures and Algorithms · Computer Science 2019-08-27 Filip Pavetić , Goran Žužić , Mile Šikić

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

The {\em shortest common superstring} and the {\em shortest common supersequence} are two well studied problems having a wide range of applications. In this paper we consider both problems with resource constraints, denoted as the…

Data Structures and Algorithms · Computer Science 2010-06-29 Raphaël Clifford , Zvi Gotthilf , Moshe Lewenstein , Alexandru Popa

Longest common extension queries (LCE queries) and runs are ubiquitous in algorithmic stringology. Linear-time algorithms computing runs and preprocessing for constant-time LCE queries have been known for over a decade. However, these…

Data Structures and Algorithms · Computer Science 2016-06-28 Maxime Crochemore , Costas S. Iliopoulos , Tomasz Kociumaka , Ritu Kundu , Solon P. Pissis , Jakub Radoszewski , Wojciech Rytter , Tomasz Waleń

The \emph{longest common extension} (\emph{LCE}) problem is to preprocess a given string $w$ of length $n$ so that the length of the longest common prefix between suffixes of $w$ that start at any two given positions is answered quickly. In…

Data Structures and Algorithms · Computer Science 2017-02-27 Yuka Tanimura , Takaaki Nishimoto , Hideo Bannai , Shunsuke Inenaga , Masayuki Takeda

We revisit the longest common extension (LCE) problem, that is, preprocess a string $T$ into a compact data structure that supports fast LCE queries. An LCE query takes a pair $(i,j)$ of indices in $T$ and returns the length of the longest…

Data Structures and Algorithms · Computer Science 2013-04-23 Philip Bille , Inge Li Goertz , Benjamin Sach , Hjalte Wedel Vildhøj

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

Palindromes are important objects in strings which have been extensively studied from combinatorial, algorithmic, and bioinformatics points of views. It is known that the length of the longest palindromic substrings (LPSs) of a given string…

Data Structures and Algorithms · Computer Science 2021-01-11 Mitsuru Funakoshi , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

Maximal Common Subsequences (MCSs) between two strings X and Y are subsequences of both X and Y that are maximal under inclusion. MCSs relax and generalize the well known and widely used concept of Longest Common Subsequences (LCSs), which…

Data Structures and Algorithms · Computer Science 2023-07-26 Alessio Conte , Roberto Grossi , Giulia Punzi , Takeaki Uno