Theory and Algorithms in Distributed Localization for Multi-Vehicle Networks Using Graph Laplacian Techniques

2019 ◽  
pp. 319-333
Author(s):  
Zhiyun Lin
Keyword(s):  
Graph Laplacian ◽  
Vehicle Networks

Mathematics of networks

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Random Walks ◽  
Adjacency Matrix ◽  
Graph Partitioning ◽  
Dynamic Networks ◽  
Graph Laplacian ◽  
Network Visualization ◽  
Final Part ◽  
Bipartite Networks ◽  
Component Structure ◽  
Basic Properties

An introduction to the mathematical tools used in the study of networks. Topics discussed include: the adjacency matrix; weighted, directed, acyclic, and bipartite networks; multilayer and dynamic networks; trees; planar networks. Some basic properties of networks are then discussed, including degrees, density and sparsity, paths on networks, component structure, and connectivity and cut sets. The final part of the chapter focuses on the graph Laplacian and its applications to network visualization, graph partitioning, the theory of random walks, and other problems.

scholarly journals Spectral Gap of the Largest Eigenvalue of the Normalized Graph Laplacian

2021 ◽  
Author(s):  
Jürgen Jost ◽  
Raffaella Mulas ◽  
Florentin Münch
Keyword(s):  
Lower Bound ◽  
Bipartite Graph ◽  
Spectral Gap ◽  
Complete Bipartite Graph ◽  
Graph Laplacian ◽  
New Method ◽  
Single Edge ◽  
Largest Eigenvalue ◽  
Complement Graph ◽  
The Largest Eigenvalue

AbstractWe offer a new method for proving that the maxima eigenvalue of the normalized graph Laplacian of a graph with n vertices is at least $$\frac{n+1}{n-1}$$ n + 1 n - 1 provided the graph is not complete and that equality is attained if and only if the complement graph is a single edge or a complete bipartite graph with both parts of size $$\frac{n-1}{2}$$ n - 1 2 . With the same method, we also prove a new lower bound to the largest eigenvalue in terms of the minimum vertex degree, provided this is at most $$\frac{n-1}{2}$$ n - 1 2 .

scholarly journals Blockchain-Based Solutions for UAV-Assisted Connected Vehicle Networks in Smart Cities: A Review, Open Issues, and Future Perspectives

Telecom ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 108-140
Author(s):  
Paulo Álvares ◽  
Lion Silva ◽  
Naercio Magaia
Keyword(s):  
Traffic Congestion ◽  
Resource Constraints ◽  
Smart Cities ◽  
The Internet ◽  
Connected Vehicle ◽  
Sensitive Data ◽  
Internet Of Vehicles ◽  
Smart Vehicles ◽  
Security Properties ◽  
Vehicle Networks

It had been predicted that by 2020, nearly 26 billion devices would be connected to the Internet, with a big percentage being vehicles. The Internet of Vehicles (IoVa) is a concept that refers to the connection and cooperation of smart vehicles and devices in a network through the generation, transmission, and processing of data that aims at improving traffic congestion, travel time, and comfort, all the while reducing pollution and accidents. However, this transmission of sensitive data (e.g., location) needs to occur with defined security properties to safeguard vehicles and their drivers since attackers could use this data. Blockchain is a fairly recent technology that guarantees trust between nodes through cryptography mechanisms and consensus protocols in distributed, untrustful environments, like IoV networks. Much research has been done in implementing the former in the latter to impressive results, as Blockchain can cover and offer solutions to many IoV problems. However, these implementations have to deal with the challenge of IoV node’s resource constraints since they do not suffice for the computational and energy requirements of traditional Blockchain systems, which is one of the biggest limitations of Blockchain implementations in IoV. Finally, these two technologies can be used to build the foundations for smart cities, enabling new application models and better results for end-users.

scholarly journals Design and Experimental Characterization of a Discovery and Tracking System for Optical Camera Communications

Sensors ◽  
2021 ◽  
Vol 21 (9) ◽  
pp. 2925
Author(s):  
Antonio Mederos-Barrera ◽  
Cristo Jurado-Verdu ◽  
Victor Guerra ◽  
Jose Rabadan ◽  
Rafael Perez-Jimenez
Keyword(s):  
Tracking System ◽  
Region Of Interest ◽  
Experimental Methodology ◽  
Visible Light Communications ◽  
Spatial Features ◽  
Tracking Algorithms ◽  
Receiver Architecture ◽  
Vehicle Networks ◽  
Time Required ◽  
Static Conditions

Visible light communications (VLC) technology is emerging as a candidate to meet the demand for interconnected devices’ communications. However, the costs of incorporating specific hardware into end-user devices slow down its market entry. Optical camera communication (OCC) technology paves the way by reusing cameras as receivers. These systems have generally been evaluated under static conditions, in which transmitting sources are recognized using computationally expensive discovery algorithms. In vehicle-to-vehicle networks and wearable devices, tracking algorithms, as proposed in this work, allow one to reduce the time required to locate a moving source and hence the latency of these systems, increasing the data rate by up to 2100%. The proposed receiver architecture combines discovery and tracking algorithms that analyze spatial features of a custom RGB LED transmitter matrix, highlighted in the scene by varying the cameras’ exposure time. By using an anchor LED and changing the intensity of the green LED, the receiver can track the light source with a slow temporal deterioration. Moreover, data bits sent over the red and blue channels do not significantly affect detection, hence transmission occurs uninterrupted. Finally, a novel experimental methodology to evaluate the evolution of the detection’s performance is proposed. With the analysis of the mean and standard deviation of novel K parameters, it is possible to evaluate the detected region-of-interest scale and centrality against the transmitter source’s ideal location.

scholarly journals Rational Krylov methods for fractional diffusion problems on graphs

2021 ◽  
Author(s):  
Michele Benzi ◽  
Igor Simunec
Keyword(s):  
Analytic Function ◽  
Diffusion Equation ◽  
Graph Laplacian ◽  
Fractional Diffusion ◽  
Singular Matrix ◽  
Krylov Methods ◽  
Fractional Powers ◽  
Directed Networks ◽  
Rank One ◽  
Diffusion Problems

AbstractIn this paper we propose a method to compute the solution to the fractional diffusion equation on directed networks, which can be expressed in terms of the graph Laplacian L as a product $$f(L^T) \varvec{b}$$ f ( L T ) b , where f is a non-analytic function involving fractional powers and $$\varvec{b}$$ b is a given vector. The graph Laplacian is a singular matrix, causing Krylov methods for $$f(L^T) \varvec{b}$$ f ( L T ) b to converge more slowly. In order to overcome this difficulty and achieve faster convergence, we use rational Krylov methods applied to a desingularized version of the graph Laplacian, obtained with either a rank-one shift or a projection on a subspace.

An Architecture for In-Vehicle Networks

2021 ◽  
pp. 1-1
Author(s):  
Jean C Walrand ◽  
Max Turner ◽  
Roy Myers
Keyword(s):  
Vehicle Networks
Sign in / Sign up

Export Citation Format

Share Document