On k-connectivity for a geometric random graph
Random Structures & Algorithms
Mobility increases the capacity of ad hoc wireless networks
IEEE/ACM Transactions on Networking (TON)
A delay-tolerant network architecture for challenged internets
Proceedings of the 2003 conference on Applications, technologies, architectures, and protocols for computer communications
Sharp thresholds For monotone properties in random geometric graphs
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Mobility improves coverage of sensor networks
Proceedings of the 6th ACM international symposium on Mobile ad hoc networking and computing
Delay of intrusion detection in wireless sensor networks
Proceedings of the 7th ACM international symposium on Mobile ad hoc networking and computing
On the cover time and mixing time of random geometric graphs
Theoretical Computer Science
The cover time of random geometric graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Combinatorics, Probability and Computing
Large Connectivity for Dynamic Random Geometric Graphs
IEEE Transactions on Mobile Computing
MANETS: High Mobility Can Make Up for Low Transmission Power
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Efficient broadcast on random geometric graphs
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A correction to the proof of a lemma in "The capacity of wireless networks"
IEEE Transactions on Information Theory
Even One-Dimensional Mobility Increases the Capacity of Wireless Networks
IEEE Transactions on Information Theory
Closing the Gap in the Capacity of Wireless Networks Via Percolation Theory
IEEE Transactions on Information Theory
Tight bounds on information dissemination in sparse mobile networks
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Viral processes by random walks on random regular graphs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Information dissemination via random walks in d-dimensional space
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Information spreading in dynamic graphs
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Opportunistic MANETs: mobility can make up for low transmission power
IEEE/ACM Transactions on Networking (TON)
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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 this paper we consider a natural extension of the random geometric graph model to the mobile setting by allowing nodes to move in space according to Brownian motion. We study three 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), coverage (the time until all points inside a finite box are detected by the network), and percolation (the time until a given node is able to communicate with the giant component of the network). We derive precise asymptotics for these problems by combining ideas from stochastic geometry, coupling and multi-scale analysis. We also give an application of our results to analyze the time to broadcast a message in a mobile network.