Related papers: Temporal Vertex Cover with a Sliding Time Window
Graph Neural Networks have gained huge interest in the past few years. These powerful algorithms expanded deep learning models to non-Euclidean space and were able to achieve state of art performance in various applications including…
Key graph-based problems play a central role in understanding network topology and uncovering patterns of similarity in homogeneous and temporal data. Such patterns can be revealed by analyzing communities formed by nodes, which in turn can…
Many real-world networks, such as transportation or trade networks, are dynamic in the sense that the edge set may change over time, but these changes are known in advance. This behavior is captured by the temporal graphs model, which has…
\emph{Temporal graphs} are a generalisation of (static) graphs, defined by a sequence of \emph{snapshots}, each a static graph defined over a common set of vertices. \emph{Exploration} problems are one of the most fundamental and most…
Time-varying networks describe a wide array of systems whose constituents and interactions evolve over time. They are defined by an ordered stream of interactions between nodes, yet they are often represented in terms of a sequence of…
In this paper, we study two generalizations of Vertex Cover and Edge Cover, namely Colorful Vertex Cover and Colorful Edge Cover. In the Colorful Vertex Cover problem, given an $n$-vertex edge-colored graph $G$ with colors from $\{1,…
The richness of many complex systems stems from the interactions among their components. The higher-order nature of these interactions, involving many units at once, and their temporal dynamics constitute crucial properties that shape the…
Numerous complex systems, such as those arisen in ecological networks, genomic contact networks, and social networks, exhibit higher-order and time-varying characteristics, which can be effectively modeled using temporal hypergraphs.…
Temporal networks are a class of time-varying networks, which change their topology according to a given time-ordered sequence of static networks (known as subsystems). This paper investigates the reachability and controllability of…
In the eternal vertex cover problem, mobile guards on the vertices of a graph are used to defend it against an infinite sequence of attacks on its edges by moving to neighbor vertices. The eternal vertex cover problem consists in…
Temporal graphs are introduced to model systems where the relationships among the entities of the system evolve over time. In this paper, we consider the temporal graphs where the edge set changes with time and all the changes are known a…
We study the complexity of the directed periodic temporal graph realization problem. This work is motivated by the design of periodic schedules in public transport with constraints on the quality of service. Namely, we require that the…
Temporal graphs are graphs whose edges are labelled with times at which they are active. Their time-sensitivity provides a useful model of real networks, but renders many problems studied on temporal graphs more computationally complex than…
We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of…
Connectivity of temporal graphs has been widely studied both as graph theory and as gossip theory. In particular, it is well known that in order to connect every vertex to every other, a temporal graph needs to have at least $2n-4$ edges…
The sparsest cut problem consists of identifying a small set of edges that breaks the graph into balanced sets of vertices. The normalized cut problem balances the total degree, instead of the size, of the resulting sets. Applications of…
Given a directed graph and a source vertex, the fully dynamic single-source reachability problem is to maintain the set of vertices that are reachable from the given vertex, subject to edge deletions and insertions. It is one of the most…
In recent years, there has been an increasing interest in the use of graph neural networks (GNNs) for analyzing dynamic graphs, which are graphs that evolve over time. However, there is still a lack of understanding of how different…
Evolving relations in real-world networks are often modelled by temporal graphs. Temporal Graph Neural Networks (TGNNs) emerged to model evolutionary behaviour of such graphs by leveraging the message passing primitive at the core of Graph…
Real-time analysis of graphs containing temporal information, such as social media streams, Q&A networks, and cyber data sources, plays an important role in various applications. Among them, detecting patterns is one of the fundamental…