Related papers: Reducing approximate Longest Common Subsequence to…

We revisit the classic combinatorial pattern matching problem of finding a longest common subsequence (LCS). For strings $x$ and $y$ of length $n$, a textbook algorithm solves LCS in time $O(n^2)$, but although much effort has been spent,…

In many applications, it is necessary to determine the similarity of two strings. A widely-used notion of string similarity is the edit distance: the minimum number of insertions, deletions, and substitutions required to transform one…

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…

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…

The Shortest Common Superstring (SCS) problem is a fundamental task in sequence analysis. In genome assembly, however, the double-stranded nature of DNA implies that each fragment may occur either in its original orientation or as its…

Analyzing patterns in data streams generated by network traffic, sensor networks, or satellite feeds is a challenge for systems in which the available storage is limited. In addition, real data is noisy, which makes designing data stream…

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…

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 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.…

We propose an algorithm for approximative dictionary lookup, where altered strings are matched against reference forms. The algorithm makes use of a divergence function between strings -- broadly belonging to the family of edit distances;…

We study the problem of computing similarity joins under edit distance on a set of strings. Edit similarity joins is a fundamental problem in databases, data mining and bioinformatics. It finds important applications in data cleaning and…

For any $T \geq 1$, there are constants $R=R(T) \geq 1$ and $\zeta=\zeta(T)>0$ and a randomized algorithm that takes as input an integer $n$ and two strings $x,y$ of length at most $n$, and runs in time $O(n^{1+\frac{1}{T}})$ and outputs an…

We show that the edit distance between two strings of length $n$ can be computed within a factor of $f(\epsilon)$ in $n^{1+\epsilon}$ time as long as the edit distance is at least $n^{1-\delta}$ for some $\delta(\epsilon) > 0$.

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…

Given two strings $A[1..n]$ and $B[1..m]$, and a set of operations allowed to edit the strings, the edit distance between $A$ and $B$ is the minimum number of operations required to transform $A$ into $B$. Sequentially, a standard Dynamic…

The edit distance between strings classically assigns unit cost to every character insertion, deletion, and substitution, whereas the Hamming distance only allows substitutions. In many real-life scenarios, insertions and deletions…

We study the average edit distance between two random strings. More precisely, we adapt a technique introduced by Lueker in the context of the average longest common subsequence of two random strings to improve the known upper bound on the…

In the Shortest-Superstring problem, we are given a set of strings S and want to find a string that contains all strings in S as substrings and has minimum length. This is a classical problem in approximation and the best known…

The problem of finding a center string that is `close' to every given string arises and has many applications in computational biology and coding theory. This problem has two versions: the Closest String problem and the Closest Substring…

We propose efficient algorithms for enumerating maximal common subsequences (MCSs) of two strings. Efficiency of the algorithms are estimated by the preprocessing-time, space, and delay-time complexities. One algorithm prepares a…