English
Related papers

Related papers: $LCSk$++: Practical similarity metric for long str…

200 papers

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

Suppose we want to seek the longest common subsequences (LCSs) of two strings as informative patterns that explain the relationship between the strings. The dynamic programming algorithm gives us a table from which all LCSs can be extracted…

Data Structures and Algorithms · Computer Science 2025-05-23 Yoshifumi Sakai

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

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

The length of the longest common subsequences (LCSs) is often used as a similarity measurement to compare two (or more) random words. Below we study its statistical behavior in mean and variance using a Monte-Carlo approach from which we…

Probability · Mathematics 2017-05-22 Qingqing Liu , Christian Houdré

This study aims to publish a novel similarity metric to increase the speed of comparison operations. Also the new metric is suitable for distance-based operations among strings. Most of the simple calculation methods, such as string length…

Data Structures and Algorithms · Computer Science 2014-01-28 Sadi Evren Seker , Oguz Altun , Uğur Ayan , Cihan Mert

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

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

Data Structures and Algorithms · Computer Science 2015-05-26 Daxin Zhu , Lei Wang , Yingjie Wu , Xiaodong Wang

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 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

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

Non-parametric entropy estimation on sequential data is a fundamental tool in signal processing, capturing information flow within or between processes to measure predictability, redundancy, or similarity. Methods based on longest common…

Data Structures and Algorithms · Computer Science 2025-10-16 Bridget Smart , Max Ward , Matthew Roughan

This study develops an algorithm to solve a variation of the Shortest Common Superstring (SCS) problem. There are two modifications to the base SCS problem. First, one string in the set S is allowed to have up to K mistakes, defined as not…

Data Structures and Algorithms · Computer Science 2024-11-05 Arthur Gilfanov

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

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 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

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

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

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

The 2-LCPS problem, first introduced by Chowdhury et al. [Fundam. Inform., 129(4):329-340, 2014], asks one to compute (the length of) a longest palindromic common subsequence between two given strings $A$ and $B$. We show that the 2-LCPS…

Data Structures and Algorithms · Computer Science 2016-12-23 Shunsuke Inenaga , Heikki Hyyrö