Latency and capacity optimal broadcasting in wireless multihop networks
ICC'09 Proceedings of the 2009 IEEE international conference on Communications
On the fundamental limits of broadcasting in wireless mobile networks
INFOCOM'10 Proceedings of the 29th conference on Information communications
On the data gathering capacity and latency wireless sensor networks
IEEE Journal on Selected Areas in Communications - Special issue on simple wireless sensor networking solutions
Efficient broadcast on random geometric graphs
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
IEEE Transactions on Communications
Broadcast analysis in dense duty-cycle sensor networks
Proceedings of the 6th International Conference on Ubiquitous Information Management and Communication
Diameter and broadcast time of random geometric graphs in arbitrary dimensions
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
The fundamental limits of broadcasting in dense wireless mobile networks
Wireless Networks
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The unit ball random geometric graph $G=G^d_p(\lambda,n)$ has as its vertices n points distributed independently and uniformly in the unit ball in ${\Bbb R}^d$, with two vertices adjacent if and only if their ℓp-distance is at most λ. Like its cousin the Erdos-Renyi random graph, G has a connectivity threshold: an asymptotic value for λ in terms of n, above which G is connected and below which G is disconnected. In the connected zone we determine upper and lower bounds for the graph diameter of G. Specifically, almost always, ${\rm diam}_p({\bf B})(1-o(1))/\lambda\leq {\rm diam}(G) \leq {\rm diam}_p({\bf B})(1+O((\ln \ln n/{\rm ln}\,n)^{1/d}))/\lambda$, where ${\rm diam}_p({\bf B})$ is the ℓp-diameter of the unit ball B. We employ a combination of methods from probabilistic combinatorics and stochastic geometry.