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Conditions for Unique Localizability in Cooperative Localization of Wireless ad hoc and Sensor Networks
Published in Chao Gao, Guorong Zhao, Hassen Fourati, Cooperative Localization and Navigation, 2019
For instance, a sensor node has a sensing/communication link, naturally, with other sensor nodes in its sensing/communication range. This results in disc graphs to model the associated network. A closely related graph structure to disc graphs is a random geometric graph, and it is used to model sensor networks. There are also applications in which some sensor nodes are distributed closely, forming clustered graphs.
Performance and robustness of discrete and finite time average consensus algorithms
Published in International Journal of Systems Science, 2018
Luca Faramondi, Roberto Setola, Gabriele Oliva
In order to assess the effective performance of the algorithms presented in the previous section, we analyse via simulations, with respect to different topologies; specifically, we consider: (i) the undirected line, where all nodes are attached sequentially on a line. This topology has the largest possible diameter , and represents the worst case for those algorithms that depend on the diameter (in the following figures we show the results for this topology with black stars). (ii) The undirected star, where a central node is attached to all other nodes, and each node is attached to just the central node. This topology, except for the complete graph, has the smallest possible diameter , hence it represents the best case for the algorithms that depend on δ (we use a magenta dashed line in the figures in this section). (iii) The Erdös–Rény random graph model (Erdos & Rényi, 1960), where any pair of nodes is connected with a probability p. Within this model, the nodes tend to be homogeneous in terms of degree and other topological properties. With respect to this network, we denote p as the density of the graph, noting that the graph becomes denser and denser as p tends to one (in the following we report the results for this network with a red dotted line). (iv) The Bárabasi–Albert Scale-Free model (Albert & Barabási, 2002), where the network is created starting from a complete graph with nodes, while the remaining n−m nodes are attached to the network one after another. Each new node is attached to m of the previous nodes, with a probability proportional to their degree. Within this network there is a strong imbalance between the degrees of the nodes; specifically, we have few highly connected nodes (i.e. the hubs) and several nodes with few links. The presence of the hubs contributes to the fast spreading of information across the network. In this case, we denote as the density of the graph (in the figures below, we use a green dotted line to represent this network). (v) The Random Geometric Graphs (Penrose, 2003), where the nodes are created in uniformly random positions in a Euclidean space (e.g. in ) and each pair of nodes is connected provided that their Euclidean distance is less than a threshold ρ. These networks represent with a good approximation a situation where a set of wireless nodes have each a communication radius, and are able to communicate only with those nodes that fall within such a radius. In this case, we denote ρ as the density of the graph, and we report the results for this topology in the figures below with a blue solid line.