Mobile geometric graphs: detection, coverage and percolation
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
On the lifetime of node-to-node communication in wireless ad hoc networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
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We provide the first rigorous analytical results for the connectivity of dynamic random geometric graphs—a model for mobile wireless networks in which vertices move in random directions in the unit torus. The model presented here follows the one described in [11]. We provide precise asymptotic results for the expected length of the connectivity and disconnectivity periods of the network. We believe that the formal tools developed in this work could be extended to be used in more concrete settings and in more realistic models, in the same manner as the development of the connectivity threshold for static random geometric graphs has affected a lot of research done on ad hoc networks.