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
Approximating the Stretch Factor of Euclidean Graphs
SIAM Journal on Computing
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
The capacity of wireless networks
IEEE Transactions on Information Theory
On the cover time and mixing time of random geometric graphs
Theoretical Computer Science
Energy efficient randomised communication in unknown AdHoc networks
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Broadcasting in udg radio networks with unknown topology
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Evaluating motion graphs for character animation
ACM Transactions on Graphics (TOG)
Energy-optimal distributed algorithms for minimum spanning trees
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
On Radio Broadcasting in Random Geometric Graphs
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
Energy efficient randomised communication in unknown AdHoc networks
Theoretical Computer Science
Secure group communication in wireless mesh networks
Ad Hoc Networks
Bootstrapping a hop-optimal network in the weak sensor model
ACM Transactions on Algorithms (TALG)
Sensitivity of critical transmission ranges to node placement distributions
IEEE Journal on Selected Areas in Communications - Special issue on stochastic geometry and random graphs for the analysis and designof wireless networks
Energy-optimal distributed algorithms for minimum spanning trees
IEEE Journal on Selected Areas in Communications - Special issue on stochastic geometry and random graphs for the analysis and designof wireless networks
Finite random geometric graphs by circular and square coverage
WiOPT'09 Proceedings of the 7th international conference on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks
IEEE Transactions on Information Theory
Proceedings of the ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Efficient distributed random walks with applications
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Results on finite wireless networks on a line
IEEE Transactions on Communications
IEEE Transactions on Communications
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
Balanced cut approximation in random geometric graphs
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Lower bounds for clear transmissions in radio networks
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
BALLAST: a ball-based algorithm for structural motifs
RECOMB'12 Proceedings of the 16th Annual international conference on Research in Computational Molecular Biology
On the impact of transmission radius on routing efficiency
Proceedings of the first ACM MobiHoc workshop on Airborne Networks and Communications
Queueing Systems: Theory and Applications
Randomized algorithms and probabilistic analysis in wireless networking
SAGA'07 Proceedings of the 4th international conference on Stochastic Algorithms: foundations and applications
Initializing sensor networks of non-uniform density in the weak sensor model
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Robust localization from incomplete local information
IEEE/ACM Transactions on Networking (TON)
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We study the emerging phenomenon of ad hoc, sensor-based communication networks. The communication is modeled by the geometric random graph model G(n, r, ℓ) where n points randomly placed within [0, ℓ]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, ℓ) of interest: connectivity, coverage, and routing-stretch. Our main contribution is a simple analysis technique we call bin-covering that we apply uniformly to get first known, (asymptotically) tight thresholds for each of these properties. Typically, in the past, geometric random 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 networking community that has seen a recent increase in the study of geometric random graphs motivated by engineering ad hoc networks.