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The longest square subsequence (LSS) problem consists of computing a longest subsequence of a given string $S$ that is a square, i.e., a longest subsequence of form $XX$ appearing in $S$. It is known that an LSS of a string $S$ of length…

Data Structures and Algorithms · Computer Science 2020-07-30 Takafumi Inoue , Shunsuke Inenaga , Hideo Bannai

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

Let $A$ and $B$ be two number sequences of length $n$ and $m$, respectively, where $m\le n$. Given a positive number $\delta$, a common almost increasing sequence $s_1\ldots s_k$ is a common subsequence for both $A$ and $B$ such that for…

Data Structures and Algorithms · Computer Science 2025-05-08 Md Tanzeem Rahat , Md. Manzurul Hasan , Debajyoti Mondal

Calculating the length of a longest common subsequence (LCS) of two strings $A$ and $B$ of length $n$ and $m$ is a classic research topic, with many worst-case oriented results known. We present two algorithms for LCS length calculation…

Data Structures and Algorithms · Computer Science 2014-05-22 Szymon Grabowski

In this paper we define a new problem, motivated by computational biology, $LCSk$ aiming at finding the maximal number of $k$ length $substrings$, matching in both input strings while preserving their order of appearance. The traditional…

Data Structures and Algorithms · Computer Science 2014-02-11 Gary Benson , Avivit Levy , Riva Shalom

In this paper we address the longest common extension (LCE) problem: to compute the length $\ell$ of the longest common prefix between any two suffixes of $T\in \Sigma^n$ with $ \Sigma = \{0, \ldots \sigma-1\} $. We present two fast and…

Data Structures and Algorithms · Computer Science 2016-07-25 Alberto Policriti , Nicola Prezza

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

We present a practical algorithm for the cyclic longest common subsequence (CLCS) problem that runs in O(mn) time, where m and n are the lengths of the two input strings. While this is not necessarily an asymptotic improvement over the…

Data Structures and Algorithms · Computer Science 2012-08-17 Andy Nguyen

We give a sublinear quantum algorithm for the longest common substring (LCS) problem on the run-length encoded (RLE) inputs, under the assumption that the prefix-sums of the runs are given. Our algorithm costs $\tilde{O}(n^{5/6})\cdot…

Quantum Physics · Physics 2023-10-03 Tzu-Ching Lee , Han-Hsuan Lin

Two strings of the same length are said to Cartesian-tree match (CT-match) if their Cartesian-trees are isomorphic [Park et al., TCS 2020]. Cartesian-tree matching is a natural model that allows for capturing similarities of numerical…

Data Structures and Algorithms · Computer Science 2026-01-01 Taketo Tsujimoto , Yuki Yonemoto , Hiroki Shibata , Takuya Mieno , Yuto Nakashima , Shunsuke Inenaga

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

In this paper we address the constrained longest common subsequence problem. Given two sequences $X$, $Y$ and a constrained sequence $P$, a sequence $Z$ is a constrained longest common subsequence for $X$ and $Y$ with respect to $P$ if $Z$…

Data Structures and Algorithms · Computer Science 2021-03-05 Francis Yuk Lun Chin , Ngai Lam Ho , Alfredo De Santis , S. K. Kim

Due to the increased availability of large datasets of biological sequences, the tools for sequence comparison are now relying on efficient alignment-free approaches to a greater extent. Most of the alignment-free approaches require the…

Data Structures and Algorithms · Computer Science 2018-07-23 F. Garofalo , G. Rosone , M. Sciortino , D. Verzotto

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

We give a near-optimal quantum algorithm for the longest common substring (LCS) problem between two run-length encoded (RLE) strings, with the assumption that the prefix-sums of the run-lengths are given. Our algorithm costs…

Quantum Physics · Physics 2024-11-06 Tzu-Ching Lee , Han-Hsuan Lin

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 consider labeled directed graphs where each vertex is labeled with a non-empty string. Such labeled graphs are also known as non-linear texts in the literature. In this paper, we introduce a new problem of comparing two given labeled…

Data Structures and Algorithms · Computer Science 2023-07-18 Yuki Yonemoto , Yuto Nakashima , Shunsuke Inenaga

Frequent pattern mining is widely used to find ``important'' or ``interesting'' patterns in data. While it is not easy to mathematically define such patterns, maximal frequent patterns are promising candidates, as frequency is a natural…

Data Structures and Algorithms · Computer Science 2025-04-08 Giovanni Buzzega , Alessio Conte , Yasuaki Kobayashi , Kazuhiro Kurita , Giulia Punzi

Computation on compressed strings is one of the key approaches to processing massive data sets. We consider local subsequence recognition problems on strings compressed by straight-line programs (SLP), which is closely related to…

Data Structures and Algorithms · Computer Science 2011-11-10 Alexander Tiskin