Related papers: Optimal shattering of complex networks
We use Hartnell's model for virus spread on a graph, also known as firefighting. For rooted trees, we propose an Unburning Algorithm, a type of greedy algorithm starting from the leaves and working back towards the root. We show that the…
We give the first polynomial-time, differentially node-private, and robust algorithm for estimating the edge density of Erd\H{o}s-R\'enyi random graphs and their generalization, inhomogeneous random graphs. We further prove…
Optimal strategies for epidemic containment are focused on dismantling the contact network through effective immunization with minimal costs. However, network fragmentation is seldom accessible in practice and may present extreme side…
The pivotal quality of proximity graphs is connectivity, i.e. all nodes in the graph are connected to one another either directly or via intermediate nodes. These types of graphs are robust, i.e., they are able to function well even if they…
Several recent studies have tackled the issue of optimal network immunization by providing efficient criteria to identify key nodes to be removed in order to break apart a network, thus preventing the occurrence of extensive epidemic…
Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…
Graph neural networks (GNNs) have attracted increasing interests. With broad deployments of GNNs in real-world applications, there is an urgent need for understanding the robustness of GNNs under adversarial attacks, especially in realistic…
Maximizing the damage by attacking specific nodes of the combat network can efficiently disrupt enemies' defense capability, protect our critical units, and enhance the resistance to the destruction of system-of-system~(SOS). However, the…
The design of an efficient curing policy, able to stem an epidemic process at an affordable cost, has to account for the structure of the population contact network supporting the contagious process. Thus, we tackle the problem of…
We study the problem of learning the structure of an optimal Bayesian network when additional constraints are posed on the network or on its moralized graph. More precisely, we consider the constraint that the network or its moralized graph…
There are many methods to find a maximum (or maximal) clique in large networks. Due to the nature of combinatorics, computation becomes exponentially expensive as the number of vertices in a graph increases. Thus, there is a need for…
Computer or communication networks are so designed that they do not easily get disrupted under external attack and, moreover, these are easily reconstructible if they do get disrupted. These desirable properties of networks can be measured…
Sampling technique has become one of the recent research focuses in the graph-related fields. Most of the existing graph sampling algorithms tend to sample the high degree or low degree nodes in the complex networks because of the…
We investigate the trade-off between the robustness against random and targeted removal of nodes from a network. To this end we utilize the stochastic block model to study ensembles of infinitely large networks with arbitrary large-scale…
The way diseases spread through schools, epidemics through countries, and viruses through the Internet is crucial in determining their risk. Although each of these threats has its own characteristics, its underlying network determines the…
Graphs are pervasive in our everyday lives, with relevance to biology, the internet, and infrastructure, as well as numerous other applications. It is thus necessary to have an understanding as to how quickly a graph disintegrates, whether…
All possible removals of $n=5$ nodes from networks of size $N=100$ are performed in order to find the optimal set of nodes which fragments the original network into the smallest largest connected component. The resulting attacks are ordered…
Despite achieving strong performance in semi-supervised node classification task, graph neural networks (GNNs) are vulnerable to adversarial attacks, similar to other deep learning models. Existing researches focus on developing either…
Subgraphs reveal information about the geometry and functionalities of complex networks. For scale-free networks with unbounded degree fluctuations, we obtain the asymptotics of the number of times a small connected graph occurs as a…
We present a strongly polynomial-time algorithm to generate bandwidth optimal allgather/reduce-scatter on any network topology, with or without switches. Our algorithm constructs pipeline schedules achieving provably the best possible…