Sharp thresholds for relative neighborhood graphs in wireless ad hoc networks

Authors:
Chih-Wei Yi;Peng-Jun Wan;Lixin Wang;Chao-Min Su
Affiliations:
Department of Computer Science, National Chiao Tung University, Hsinchu City, Taiwan;Department of Computer Science, Illinois Institute of Technology, Chicago, IL;Department of Computer Science, Illinois Institute of Technology, Chicago, IL;Department of Computer Science, National Chiao Tung University, Hsinchu City, Taiwan
Venue:
IEEE Transactions on Wireless Communications
Year:
2010

Citing 7
Cited 0

GPSR: greedy perimeter stateless routing for wireless networks

MobiCom '00 Proceedings of the 6th annual international conference on Mobile computing and networking
Routing with guaranteed delivery in ad hoc wireless networks

Wireless Networks
On the Spanning Ratio of Gabriel Graphs and beta-skeletons

LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
The Critical Transmitting Range for Connectivity in Sparse Wireless Ad Hoc Networks

IEEE Transactions on Mobile Computing
Sharp thresholds For monotone properties in random geometric graphs

STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Geometrically aware communication in random wireless networks

Proceedings of the twenty-third annual ACM symposium on Principles of distributed 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

Quantified Score

Hi-index	0.01

Visualization

Abstract

In wireless ad hoc networks, relative neighborhood graphs (RNGs) are widely used for topology control. If every node has the same transmission radius, then an RNG can be locally constructed by using only one hop information if the transmission radius is set no less than the largest edge length of the RNG. The largest RNG edge length is called the critical transmission radius for the RNG. In this paper, we consider the RNG over a Poisson point process with mean density n in a unit-area disk. Let β0 = √1/ (2/3 - √3/2π) ≈ 1.6. We show that the largest RNG edge length is asymptotically almost surely at most β√ln n/πn for any fixed β β0 and at least β√lnn/πn for any fixed β 0. This implies that the threshold width of the critical transmission radius is o(√lnn/n). In addition, we also prove that for any constant ξ, the expected number of RNG edges whose lengths are not less than β0√lnn + ξ/πn is asymptotically equal to β02/2 e-ξ.