Related papers: Heaven & Hell: One-Step Hub Consensus
This paper explores the fundamental properties of distributed minimization of a sum of functions with each function only known to one node, and a pre-specified level of node knowledge and computational capacity. We define the optimization…
Monitoring tasks, such as anomaly and DDoS detection, require identifying frequent flow aggregates based on common IP prefixes. These are known as \emph{hierarchical heavy hitters} (HHH), where the hierarchy is determined based on the type…
Graphs with heterophily, where adjacent nodes carry different labels, are prevalent in real-world applications, from social networks to molecular interactions. However, existing spectral Graph Neural Network (GNN) approaches tailored for…
Graph Neural Networks (GNNs) have achieved great success but are often considered to be challenged by varying levels of homophily in graphs. Recent \textit{empirical} studies have surprisingly shown that homophilic GNNs can perform well…
The dangling nodes is the nodes with no out-links in the web graph. It saves many computational cost and operations provided the dangling nodes are lumped into one node. In this paper, motivated by so many dangling nodes in web graph, we…
In this paper, we study the behaviour of the generalized power domination number of a graph by small changes on the graph, namely edge and vertex deletion and edge contraction. We prove optimal bounds for $\gamma\_{p,k}(G-e)$,…
Group testing, a problem with diverse applications across multiple disciplines, traditionally assumes independence across nodes' states. Recent research, however, focuses on real-world scenarios that often involve correlations among nodes,…
A vertex of a randomly growing graph is called a persistent hub if at all but finitely many moments of time it has the maximal degree in the graph. We establish the existence of a persistent hub in the Barab\'asi--Albert random graph model…
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…
Higher-order networks encode the many-body interactions of complex systems ranging from the brain to biological transportation networks. Simplicial and cell complexes are ideal higher-order network representations for investigating…
Direct policy search has been widely applied in modern reinforcement learning and continuous control. However, the theoretical properties of direct policy search on nonsmooth robust control synthesis have not been fully understood. The…
Given a network represented by a weighted directed graph G, we consider the problem of finding a bounded cost set of nodes S such that the influence spreading from S in G, within a given time bound, is as large as possible. The dynamic that…
Network controllability robustness reflects how well a networked dynamical system can maintain its controllability against destructive attacks. This paper investigates the network controllability robustness from the perspective of a…
We introduce a model for innovation-, evolution- and opinion dynamics whose spreading is dictated by unanimity rules, i.e. a node will change its (binary) state only if all of its neighbours have the same corresponding state. It is shown…
Recent interest in the external validity of prediction models (i.e., the problem of different train and test distributions, known as dataset shift) has produced many methods for finding predictive distributions that are invariant to dataset…
Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet…
Let $G$ be a graph and ${\mathcal{\tau}}: V(G)\rightarrow \Bbb{N}\cup \{0\}$ be an assignment of thresholds to the vertices of $G$. A subset of vertices $D$ is said to be a dynamic monopoly corresponding to $(G, \tau)$ if the vertices of…
Graph Neural Networks (GNNs) excel in delineating graph structures in diverse domains, including community analysis and recommendation systems. As the interpretation of GNNs becomes increasingly important, the demand for robust baselines…
Distributed consensus protocols provide a mechanism for spreading information within clustered networks, allowing agents and clusters to make decisions without requiring direct access to the state of the ensemble. In this work, we propose a…
In this paper, we consider the $\mathcal{H}_2$-norm of networked systems with multi-time scale consensus dynamics and vector-valued agent states. This allows us to explore how measurement and process noise affect consensus on…