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We consider the longest common subsequence (LCS) problem with the restriction that the common subsequence is required to consist of at least $k$ length substrings. First, we show an $O(mn)$ time algorithm for the problem which gives a…

Data Structures and Algorithms · Computer Science 2017-02-07 Yohei Ueki , Diptarama , Masatoshi Kurihara , Yoshiaki Matsuoka , Kazuyuki Narisawa , Ryo Yoshinaka , Hideo Bannai , Shunsuke Inenaga , Ayumi Shinohara

We provide a deterministic algorithm that outputs an $O(n^{3/4} \log n)$-approximation for the Longest Common Subsequence (LCS) of two input sequences of length $n$ in near-linear time. This is the first deterministic approximation…

Data Structures and Algorithms · Computer Science 2025-07-31 Itai Boneh , Shay Golan , Matan Kraus

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

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 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

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

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

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 edit distance (ED) and longest common subsequence (LCS) are two fundamental problems which quantify how similar two strings are to one another. In this paper, we consider these problems in the asymmetric streaming model introduced by…

Data Structures and Algorithms · Computer Science 2020-04-17 Alireza Farhadi , MohammadTaghi Hajiaghayi , Aviad Rubinstein , Saeed Seddighin

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

The nature of the alignment with gaps corresponding to a longest common subsequence (LCS) of two independent iid random sequences drawn from a finite alphabet is investigated. It is shown that such an optimal alignment typically matches…

Probability · Mathematics 2016-04-22 C. Houdré , H. Matzinger

We study the problem of aligning multiple sequences with the goal of finding an alignment that either maximizes the number of aligned symbols (the longest common subsequence (LCS)), or minimizes the number of unaligned symbols (the…

Data Structures and Algorithms · Computer Science 2021-10-26 Debarati Das , Barna Saha

In this paper, we revisit the much studied LCS problem for two given sequences. Based on the algorithm of Iliopoulos and Rahman for solving the LCS problem, we have suggested 3 new improved algorithms. We first reformulate the problem in a…

Data Structures and Algorithms · Computer Science 2015-08-25 Daxin Zhu , Lei Wang , Yingjie Wu , Xiaodong Wang

The longest common subsequence (LCS) problem is a central problem in stringology that finds the longest common subsequence of given two strings $A$ and $B$. More recently, a set of four constrained LCS problems (called generalized…

Data Structures and Algorithms · Computer Science 2020-01-17 Kohei Yamada , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

Estimating the length of the longest increasing subsequence (LIS) in an array is a problem of fundamental importance. Despite the significance of the LIS estimation problem and the amount of attention it has received, there are important…

Data Structures and Algorithms · Computer Science 2021-02-12 Ilan Newman , Nithin Varma

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

Longest Common Substring (LCS) is an important text processing problem, which has recently been investigated in the quantum query model. The decisional version of this problem, LCS with threshold $d$, asks whether two length-$n$ input…

Data Structures and Algorithms · Computer Science 2022-11-30 Ce Jin , Jakob Nogler

This study investigates whether reoptimization can help in solving the closest substring problem. We are dealing with the following reoptimization scenario. Suppose, we have an optimal l-length closest substring of a given set of sequences…

Data Structures and Algorithms · Computer Science 2017-03-21 Jhoirene B. Clemente , Henry N. Adorna

One of the most fundamental method for comparing two given strings $A$ and $B$ is the longest common subsequence (LCS), where the task is to find (the length) of an LCS of $A$ and $B$. In this paper, we deal with the STR-IC-LCS problem…

Data Structures and Algorithms · Computer Science 2024-05-21 Yuki Yonemoto , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai

The Lattice String Approximation algorithm (or LSA algorithm) of M. L. Lapidus and M. van Frankenhuijsen is a procedure that approximates the complex dimensions of a nonlattice self-similar fractal string by the complex dimensions of a…

Number Theory · Mathematics 2023-06-26 Michel L. Lapidus , Machiel van Frankenhuijsen , Edward K. Voskanian