On the connectivity of a random interval graph
Proceedings of the seventh international conference on Random structures and algorithms
Unreliable sensor grids: coverage, connectivity and diameter
Ad Hoc Networks
The capacity of wireless networks
IEEE Transactions on Information Theory
Extremal Properties of Three-Dimensional Sensor Networks with Applications
IEEE Transactions on Mobile Computing
The bin-covering technique for thresholding random geometric graph properties
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On the cover time and mixing time of random geometric graphs
Theoretical Computer Science
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Trade-offs between mobility and density for coverage in wireless sensor networks
Proceedings of the 13th annual ACM international conference on Mobile computing and networking
Distance graphs: from random geometric graphs to Bernoulli graphs and between
Proceedings of the fifth international workshop on Foundations of mobile computing
Combinatorics, Probability and Computing
ACM Transactions on Sensor Networks (TOSN)
A survey of message diffusion protocols in mobile ad hoc networks
Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools
Bootstrapping a hop-optimal network in the weak sensor model
ACM Transactions on Algorithms (TALG)
Sharp thresholds for relative neighborhood graphs in wireless ad hoc networks
IEEE Transactions on Wireless Communications
Thresholding random geometric graph properties motivated by ad hoc sensor networks
Journal of Computer and System Sciences
Phase transition width of connectivity of wireless multi-hop networks in shadowing environment
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
On the cover time of random geometric graphs
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Bootstrapping a hop-optimal network in the weak sensor model
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Mobile geometric graphs: detection, coverage and percolation
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Energy-efficient markov chain-based duty cycling schemes for greener wireless sensor networks
ACM Journal on Emerging Technologies in Computing Systems (JETC)
Randomized algorithms and probabilistic analysis in wireless networking
SAGA'07 Proceedings of the 4th international conference on Stochastic Algorithms: foundations and applications
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Random geometric graphs result from taking n uniformly distributed points in the unit cube, [0,1]d, and connecting two points if their Euclidean distance is at most r, for some prescribed r. We show that monotone properties for this class of graphs have sharp thresholds by reducing the problem to bounding the bottleneck matching on two sets of $n$ points distributed uniformly in [0,1]d. We present upper bounds on the threshold width, and show that our bound is sharp for d = 1 and at most a sublogarithmic factor away for d ≥ 2. Interestingly, the threshold width is much sharper for random geometric graphs than for Bernoulli random graphs. Further, a random geometric graph is shown to be a subgraph, with high probability, of another independently drawn random geometric graph with a slightly larger radius; this property is shown to have no analogue for Bernoulli random graphs.