GPSR: greedy perimeter stateless routing for wireless networks
MobiCom '00 Proceedings of the 6th annual international conference on Mobile computing and networking
On greedy geographic routing algorithms in sensing-covered networks
Proceedings of the 5th ACM international symposium on Mobile ad hoc networking and computing
Asymptotic critical transmission radius for greedy forward routing in wireless ad hoc networks
Proceedings of the 7th ACM international symposium on Mobile ad hoc networking and computing
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Geographic routing in d-dimensional spaces with guaranteed delivery and low stretch
IEEE/ACM Transactions on Networking (TON)
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In wireless ad hoc networks, greedy forward routing is a localized geographic routing algorithm in which one node discards a packet if none of its neighbors is closer to the destination of the packet than itself, or otherwise forwards the packet to the neighbor closest to the destination. If all nodes have the same transmission radii, the critical transmission radius for greedy forward routing is the smallest transmission radius which ensures packets can be delivered by greedy forward routing through any source-destination pair. In this paper, we study asymptotic critical transmission radii of randomly deployed wireless ad hoc networks. Assume network nodes are represented by a Poisson point process of density n over a unit-area convex compact region whose boundary curvature is bounded. We show that the ratio of critical transmission radii to √lnn/πn is asymptotically almost surely equal to √1/(2/3 - √3/2π) ≅ 1.6.