On k-connectivity for a geometric random graph
Random Structures & Algorithms
The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Highly-resilient, energy-efficient multipath routing in wireless sensor networks
ACM SIGMOBILE Mobile Computing and Communications Review
Approximating the Stretch Factor of Euclidean Graphs
SIAM Journal on Computing
Random Geometric Problems on [0, 1]²
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
The Critical Transmitting Range for Connectivity in Sparse Wireless Ad Hoc Networks
IEEE Transactions on Mobile Computing
Random evolution in massive graphs
Handbook of massive data sets
Sharp thresholds For monotone properties in random geometric graphs
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Efficient communication in an ad-hoc network
Journal of Algorithms
The web as a graph: measurements, models, and methods
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Random geometric graph diameter in the unit disk with lp metric
GD'04 Proceedings of the 12th international conference on Graph Drawing
Connectivity properties of a packet radio network model
IEEE Transactions on Information Theory
The capacity of wireless networks
IEEE Transactions on Information Theory
On the connectivity of radio networks
IEEE Transactions on Information Theory
Journal of the ACM (JACM)
| Hi-index | 0.00 |
We study the emerging phenomenon of ad hoc, sensor-based communication networks. The communication is modeled by the random geometric graph model G(n,r,@?) where n points randomly placed within [0,@?]^d form the nodes, and any two nodes that correspond to points at most distance r away from each other are connected. We study fundamental properties of G(n,r,@?) of interest: connectivity, coverage, and routing-stretch. We use a technique that we call bin-covering that we apply uniformly to get (asymptotically) tight thresholds for each of these properties. Typically, in the past, random geometric graph analyses involved sophisticated methods from continuum percolation theory; on contrast, our bin-covering approach is discrete and very simple, yet it gives us tight threshold bounds. The technique also yields algorithmic benefits as illustrated by a simple local routing algorithm for finding paths with low stretch. Our specific results should also prove interesting to the sensor networking community that has seen a recent increase in the study of random geometric graphs motivated by engineering ad hoc networks.