Related papers: Dynamic Dyck and Tree Edit Distance: Decomposition…
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 consider an efficient two-party protocol for securely computing the similarity of strings w.r.t. an extended edit distance measure. Here, two parties possessing strings $x$ and $y$, respectively, want to jointly compute an approximate…
The notion of $\mathcal{H}$-treewidth, where $\mathcal{H}$ is a hereditary graph class, was recently introduced as a generalization of the treewidth of an undirected graph. Roughly speaking, a graph of $\mathcal{H}$-treewidth at most $k$…
Quasiperiodicity in strings was introduced almost 30 years ago as an extension of string periodicity. The basic notions of quasiperiodicity are cover and seed. A cover of a text $T$ is a string whose occurrences in $T$ cover all positions…
We consider the approximate pattern matching problem under edit distance. In this problem we are given a pattern $P$ of length $w$ and a text $T$ of length $n$ over some alphabet $\Sigma$, and a positive integer $k$. The goal is to find all…
In this paper we study the fundamental problem of maintaining a dynamic collection of strings under the following operations: concat - concatenates two strings, split - splits a string into two at a given position, compare - finds the…
The edit distance is a basic string similarity measure used in many applications such as text mining, signal processing, bioinformatics, and so on. However, the computational cost can be a problem when we repeat many distance calculations…
The min-distance between two nodes $u, v$ is defined as the minimum of the distance from $v$ to $u$ or from $u$ to $v$, and is a natural distance metric in DAGs. As with the standard distance problems, the Strong Exponential Time Hypothesis…
A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…
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…
The suffix array $SA[1..n]$ of a text $T$ of length $n$ is a permutation of $\{1,\ldots,n\}$ describing the lexicographical ordering of suffixes of $T$, and it is considered to be among of the most important data structures in string…
In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…
We study the online variant of the language distance problem for two classical formal languages, the language of palindromes and the language of squares, and for the two most fundamental distances, the Hamming distance and the edit…
Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…
Several problems that are NP-hard on general graphs are efficiently solvable on graphs with bounded treewidth. Efforts have been made to generalize treewidth and the related notion of pathwidth to digraphs. Directed treewidth, DAG-width and…
We study fully dynamic algorithms for maximum matching. This is a well-studied problem, known to admit several update-time/approximation trade-offs. For instance, it is known how to maintain a 1/2-approximate matching in $\log^{O(1)} n$…
We revisit the task of computing the edit distance in sublinear time. In the $(k,K)$-gap edit distance problem the task is to distinguish whether the edit distance of two strings is at most $k$ or at least $K$. It has been established by…
In a way similar to the string-to-string correction problem we address time series similarity in the light of a time-series-to-time-series-correction problem for which the similarity between two time series is measured as the minimum cost…
Tree embedding has been a fundamental method in algorithm design with wide applications. We focus on the efficiency of building tree embedding in various computational settings under high-dimensional Euclidean $\mathbb{R}^d$. We devise a…
In this paper we design and prove correct a fully dynamic distributed algorithm for maintaining an approximate Steiner tree that connects via a minimum-weight spanning tree a subset of nodes of a network (referred as Steiner members or…