Related papers: Connectivity in Dense Networks Confined within Rig…
We find conditions for the connectivity of inhomogeneous random graphs with intermediate density. Our results generalize the classical result for G(n, p), when p = c log n/n. We draw n independent points X_i from a general distribution on a…
It is shown that a greedy orthogonal access scheme achieves the sum degrees of freedom of all one-dimensional (all nodes placed along a straight line) convex cellular networks (where cells are convex regions) when no channel knowledge is…
This paper provides a necessary and sufficient condition for a random network with nodes Poissonly distributed on a unit square and a pair of nodes directly connected following a generic random connection model to be asymptotically almost…
Consider a graph on $n$ uniform random points in the unit square, each pair being connected by an edge with probability $p$ if the inter-point distance is at most $r$. We show that as $n\to\infty$ the probability of full connectivity is…
We present a unified analytical framework within which power control, rate allocation, routing, and congestion control for wireless networks can be optimized in a coherent and integrated manner. We consider a multi-commodity flow model with…
With the rise of big data, networks have pervaded many aspects of our daily lives, with applications ranging from the social to natural sciences. Understanding the latent structure of the network is thus an important question. In this…
This paper develops a stochastic geometry-based approach for the modeling and analysis of single- and multi-cluster wireless networks. We first define finite homogeneous Poisson point processes to model the number and locations of the…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
A simple and accurate relationship is demonstrated that links the average shortest path, nodes, and edges in a complex network. This relationship takes advantage of the concept of link density and shows a large improvement in fitting…
Future wireless networks are expected to be a convergence of many diverse network technologies and architectures, such as cellular networks, wireless local area networks, sensor networks, and device to device communications. Through…
We consider arbitrary dense wireless networks, in which $n$ nodes are placed in an arbitrary (deterministic) manner on a square region of unit area and communicate with each other over Gaussian fading channels. We provide inner and outer…
Network geometry, characterized by nodes with associated latent variables, is a fundamental feature of real-world networks. Still, when only the network edges are given, it may be difficult to assess whether the network contains an…
Connectivity of wireless sensor networks (WSNs) is a fundamental global property expected to be maintained even though some sensor nodes are at fault. In this paper, we investigate the connectivity of random geometric graphs (RGGs) in the…
Much of the current theory of networked control systems uses simple point-to-point communication models as an abstraction of the underlying network. As a result, the controller has very limited information on the network conditions and…
We consider two-source two-destination (i.e., two-unicast) multi-hop wireless networks that have a layered structure with arbitrary connectivity. We show that, if the channel gains are chosen independently according to continuous…
We introduce a model for capturing the effects of beam misdirection on coverage and throughput in a directional wireless network using stochastic geometry. In networks employing ideal sector antennas without sidelobes, we find that…
k-connectivity is an important measure of network robustness and resilience to random faults and disruptions. We undertake both local and global approaches to k-connectivity and calculate closed form analytic formulas for the probability…
Motivated by potential applications in power systems, we study a problem of optimizing a sum of $n$ convex functions on dynamic networks of $n$ nodes when each function is known to only a single node. The nodes' variables, while satisfy…
The fundamental idea of embedding a network in a metric space is rooted in the principle of proximity preservation. Nodes are mapped into points of the space with pairwise distance that reflects their proximity in the network. Popular…
While the wireless word moves towards higher frequency bands, new challenges arises, due to the inherent characteristics of the transmission links, such as high path and penetration losses. Penetration losses causes blockages that in turn…