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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

In this paper, we consider a generalized longest common subsequence problem, the string-excluding constrained LCS problem. For the two input sequences $X$ and $Y$ of lengths $n$ and $m$, and a constraint string $P$ of length $r$, the…

Data Structures and Algorithms · Computer Science 2013-01-31 Lei Wang , Xiaodong Wang , Yingjie Wu , Daxin Zhu

The Longest Common Subsequence (LCS) of two strings is a fundamental string similarity measure with a classical dynamic programming solution taking quadratic time. Despite significant efforts, little progress was made in improving the…

Data Structures and Algorithms · Computer Science 2021-12-17 Negev Shekel Nosatzki

The problem of finding longest common subsequence (LCS) is one of the fundamental problems in computer science, which finds application in fields such as computational biology, text processing, information retrieval, data compression etc.…

Computational Complexity · Computer Science 2020-06-25 Amey Bhangale , Diptarka Chakraborty , Rajendra Kumar

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

In this paper, we consider a generalized longest common subsequence problem, in which a constraining sequence of length $s$ must be included as a substring and the other constraining sequence of length $t$ must be excluded as a subsequence…

Data Structures and Algorithms · Computer Science 2015-06-02 Daxin Zhu , Lei Wang , Yingjie Wu , Xiaodong Wang

We consider the communication complexity of fundamental longest common prefix (Lcp) problems. In the simplest version, two parties, Alice and Bob, each hold a string, $A$ and $B$, and we want to determine the length of their longest common…

Data Structures and Algorithms · Computer Science 2018-06-11 Philip Bille , Mikko Berggreen Ettienne , Roberto Grossi , Inge Li Gørtz , Eva Rotenberg

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 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 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

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

We consider the problem of finding, given two documents of total length $n$, a longest string occurring as a substring of both documents. This problem, known as the Longest Common Substring (LCS) problem, has a classic $O(n)$-time solution…

Data Structures and Algorithms · Computer Science 2020-04-29 Stav Ben-Nun , Shay Golan , Tomasz Kociumaka , Matan Kraus

Given two random finite sequences from $[k]^n$ such that a prefix of the first sequence is a suffix of the second, we examine the length of their longest common subsequence. If $\ell$ is the length of the overlap, we prove that the expected…

Probability · Mathematics 2018-03-12 Boris Bukh , Raymond Hogenson

Finding an Approximate Longest Common Substring (ALCS) within a given set $S=\{s_1,s_2,\ldots,s_m\}$ of $m \ge 2$ strings is a key problem in computational biology, such as identifying related mutations across multiple genetic sequences. We…

Data Structures and Algorithms · Computer Science 2025-09-22 Hamed Hasibi , Neerja Mhaskar , W. F. Smyth

In a \emph{weighted sequence}, for every position of the sequence and every letter of the alphabet a probability of occurrence of this letter at this position is specified. Weighted sequences are commonly used to represent imprecise or…

Data Structures and Algorithms · Computer Science 2017-08-28 Carl Barton , Tomasz Kociumaka , Chang Liu , Solon P. Pissis , Jakub Radoszewski

The longest common extension (LCE) of two indices in a string is the length of the longest identical substrings starting at these two indices. The LCE problem asks to preprocess a string into a compact data structure that supports fast LCE…

Data Structures and Algorithms · Computer Science 2015-07-10 Philip Bille , Pawel Gawrychowski , Inge Li Goertz , Gad M. Landau , Oren Weimann

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 prove that longest common prefix (LCP) information can be stored in much less space than previously known. More precisely, we show that in the presence of the text and the suffix array, o(n) additional bits are sufficient to answer…

Data Structures and Algorithms · Computer Science 2010-02-19 Johannes Fischer

A repetition free Longest Common Subsequence (LCS) of two sequences x and y is an LCS of x and y where each symbol may appear at most once. Let R denote the length of a repetition free LCS of two sequences of n symbols each one chosen…

Combinatorics · Mathematics 2013-05-22 Marcos Kiwi , Cristina G. Fernandes

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