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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

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

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

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

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

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 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

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

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

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

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

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

In the longest common substring (LCS) problem, we are given two strings $S$ and $T$, each of length at most $n$, and we are asked to find a longest string occurring as a fragment of both $S$ and $T$. This is a classical and well-studied…

Data Structures and Algorithms · Computer Science 2018-07-17 Amihood Amir , Panagiotis Charalampopoulos , Solon P. Pissis , Jakub Radoszewski

We study sketching and streaming algorithms for the Longest Common Subsequence problem (LCS) on strings of small alphabet size $|\Sigma|$. For the problem of deciding whether the LCS of strings $x,y$ has length at least $L$, we obtain a…

Data Structures and Algorithms · Computer Science 2018-10-03 Karl Bringmann , Bhaskar Ray Chaudhury

Finding analytically the statistics of the longest common subsequence (LCS) of a pair of random sequences drawn from c alphabets is a challenging problem in computational evolutionary biology. We present exact asymptotic results for the…

Genomics · Quantitative Biology 2009-11-10 Satya N. Majumdar , Sergei Nechaev

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

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

Data Structures and Algorithms · Computer Science 2013-03-11 Lei Wang , Xiaodong Wang , Yingjie Wu , Daxin Zhu

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

Two important similarity measures between sequences are the longest common subsequence (LCS) and the dynamic time warping distance (DTWD). The computations of these measures for two given sequences are central tasks in a variety of…

Computational Complexity · Computer Science 2015-02-02 Amir Abboud , Arturs Backurs , Virginia Vassilevska Williams

We study dynamic algorithms for the longest increasing subsequence (\textsf{LIS}) problem. A dynamic \textsf{LIS} algorithm maintains a sequence subject to operations of the following form arriving one by one: (i) insert an element, (ii)…

Data Structures and Algorithms · Computer Science 2021-03-11 Tomasz Kociumaka , Saeed Seddighin