Related papers: Longest Common Subsequence in at Least $k$ Length …

We present the first $\mathrm{o}(n)$-space polynomial-time algorithm for computing the length of a longest common subsequence. Given two strings of length $n$, the algorithm runs in $\mathrm{O}(n^{3})$ time with $\mathrm{O}\left(\frac{n…

In this paper, we consider the ``Shortest Superstring Problem''(SSP) or the ``Shortest Common Superstring Problem''(SCS). The problem is as follows. For a positive integer $n$, a sequence of n strings $S=(s^1,\dots,s^n)$ is given. We should…

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…

In the Manhattan Sequence Consensus problem (MSC problem) we are given $k$ integer sequences, each of length $l$, and we are to find an integer sequence $x$ of length $l$ (called a consensus sequence), such that the maximum Manhattan…

In the Longest Common Factor with $k$ Mismatches (LCF$_k$) problem, we are given two strings $X$ and $Y$ of total length $n$, and we are asked to find a pair of maximal-length factors, one of $X$ and the other of $Y$, such that their…

Let $X_1, X_2, ..., X_s$ and $Y_1, Y_2, ..., Y_t$ be strings over an alphabet $\Sigma$, where $s$ and $t$ are positive integers. The longest common subsequence and substring problem for multiple strings $X_1, X_2, ..., X_s$ and $Y_1, Y_2,…

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…

Let $\Sigma$ be an alphabet. For two strings $X$, $Y$, and a constrained string $P$ over the alphabet $\Sigma$, the constrained longest common subsequence and substring problem for two strings $X$ and $Y$ with respect to $P$ is to find a…

We consider the classic problem of computing the Longest Common Subsequence (LCS) of two strings of length $n$. While a simple quadratic algorithm has been known for the problem for more than 40 years, no faster algorithm has been found…

In this work, we consider a variant of the classical Longest Common Subsequence problem called Doubly-Constrained Longest Common Subsequence (DC-LCS). Given two strings s1 and s2 over an alphabet A, a set C_s of strings, and a function Co…

Palindromes are strings that read the same forward and backward. Problems of computing palindromic structures in strings have been studied for many years with a motivation of their application to biology. The longest palindrome problem is…

This paper performs the analysis necessary to bound the running time of known, efficient algorithms for generating all longest common subsequences. That is, we bound the running time as a function of input size for algorithms with time…

One of the most critical problems in the field of string algorithms is the longest common subsequence problem (LCS). The problem is NP-hard for an arbitrary number of strings but can be solved in polynomial time for a fixed number of…

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…

The longest common substring problem consists in finding a longest string that appears as a (contiguous) substring of two input strings. We consider the dynamic variant of this problem, in which we are to maintain two dynamic strings $S$…

Given a string $T$ with length $n$ whose characters are drawn from an ordered alphabet of size $\sigma$, its longest Lyndon subsequence is a longest subsequence of $T$ that is a Lyndon word. We propose algorithms for finding such a…

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…

The Shortest Common Superstring problem (SCS) consists, for a set of strings S = {s_1,...,s_n}, in finding a minimum length string that contains all s_i, 1<= i <= n, as substrings. While a 2+11/30 approximation ratio algorithm has recently…

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…

We present an algorithm computing the longest periodic subsequence of a string of length $n$ in $O(n^7)$ time with $O(n^4)$ words of space. We obtain improvements when restricting the exponents or extending the search allowing the reported…