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The two graphs of the title both have vertex set G. In the intersection power graph, x and y are joined if some non-identity element is a power of both; in the power graph, x and y joined if one is a power of the other. Thus the power graph…

Deep neural networks have recently emerged as a disruptive technology to solve NP-hard wireless resource allocation problems in a real-time manner. However, the adopted neural network structures, e.g., multi-layer perceptron (MLP) and…

In distributed computing by mobile robots, robots are deployed over a region, continuous or discrete, operating through a sequence of \textit{look-compute-move} cycles. An extensive study has been carried out to understand the computational…

The rising use of information and communication technology in smart grids likewise increases the risk of failures that endanger the security of power supply, e.g., due to errors in the communication configuration, faulty control algorithms,…

We characterize the computational power of neural networks that follow the graph neural network (GNN) architecture, not restricted to aggregate-combine GNNs or other particular types. We establish an exact correspondence between the…

Field-deployable edge computing nodes form a network and are used to complete scientific tasks for remote sensing and monitoring. The networked nodes collectively decide which scientific applications to run while they are constrained by…

Due to the fact that the numbers of annually published papers have witnessed a linear growth in some citation networks, a geometric model is thus proposed to predict some statistical features of those networks, in which the academic…

We consider wireless networks operating under the SINR model of interference. Nodes have limited individual knowledge and capabilities: they do not know their positions in a coordinate system in the plane, further they do not know their…

This paper considers a generalized framework to study OSNR optimization-based end-to-end link level power control problems in optical networks. We combine favorable features of game-theoretical approach and central cost approach to allow…

We consider the problem of inferring the functional connectivity of a large-scale computer network from sparse time series of events emitted by its nodes. We do so under the following three domain-specific constraints: (a) non-stationarity…

Classical list scheduling is a very popular and efficient technique for scheduling jobs in parallel and distributed platforms. It is inherently centralized. However, with the increasing number of processors, the cost for managing a single…

We consider distributed model-checking of Monadic Second-Order logic (MSO) on graphs which constitute the topology of communication networks. The graph is thus both the structure being checked and the system on which the distributed…

In this work, we study protocols so that populations of distributed processes can construct networks. In order to highlight the basic principles of distributed network construction we keep the model minimal in all respects. In particular,…

High-dimensional data analysis typically focuses on low-dimensional structure, often to aid interpretation and computational efficiency. Graphical models provide a powerful methodology for learning the conditional independence structure in…

We consider multivariate two-sample tests of means, where the location shift between the two populations is expected to be related to a known graph structure. An important application of such tests is the detection of differentially…

Modelling long-range dependencies is critical for scene understanding tasks in computer vision. Although CNNs have excelled in many vision tasks, they are still limited in capturing long-range structured relationships as they typically…

Distributed function computation is the problem, for a networked system of $n$ autonomous agents, to collectively compute the value $f(v_1, \ldots, v_n)$ of some input values, each initially private to one agent in the network. Here, we…

The rapid advancement of technology underscores the critical importance of robustness in complex network systems. This paper presents a framework for investigating the structural robustness of interconnected network models. This paper…

Various real-life planning problems require making upfront decisions before all parameters of the problem have been disclosed. An important special case of such problem especially arises in scheduling and staff rostering problems, where a…

Parallel betweenness computation algorithms are proposed and implemented in a graph database for power system contingency selection. Principles of the graph database and graph computing are investigated for both node and edge betweenness…