Paper Info
Title
Mobile Geometric Graphs, and Detection and Communication Problems in Mobile Wireless Networks
Abstract
Static wireless networks are by now quite well understood mathematically through the random geometric graph model. By contrast, there are relatively few rigorous results on the practically important case of mobile networks, in which the nodes move over time; moreover, these results often make unrealistic assumptions about node mobility such as the ability to make very large jumps. In this paper we consider a realistic model for mobile wireless networks which we call mobile geometric graphs, and which is a natural extension of the random geometric graph model. We study two fundamental questions in this model: detection (the time until a given "target" point - which may be either fixed or moving - is detected by the network), and percolation (the time until a given node is able to communicate with the giant component of the network). For detection, we show that the probability that the detection time exceeds t is \exp(-\Theta(t/\log t)) in two dimensions, and \exp(-\Theta(t)) in three or more dimensions, under reasonable assumptions about the motion of the target. For percolation, we show that the probability that the percolation time exceeds t is \exp(-\Omega(t^\frac{d}{d+2})) in all dimensions d\geq 2. We also give a sample application of this result by showing that the time required to broadcast a message through a mobile network with n nodes above the threshold density for existence of a giant component is O(\log^{1+2/d} n) with high probability.
Year
Venue
Keywords
2010
Clinical Orthopaedics and Related Research
random geometric graph,giant component,two dimensions,wireless network,geometric graph,mobile network,discrete mathematics
Field
DocType
Volume
Wireless network,Graph,Broadcasting,Discrete mathematics,Combinatorics,Giant component,Omega,Cellular network,Random geometric graph,Percolation,Mathematics
Journal
abs/1005.1
Citations 
PageRank 
References 
3
0.50
13
Authors
2
Name
Order
Citations
PageRank
Alistair Sinclair11506308.40
Alexandre O. Stauffer213011.34