On the longest edge of Gabriel graphs in wireless ad hoc networks

IEEE Transactions on Parallel and Distributed Systems

Volumn 18, Issue 1, 2007, Pages 111-125

  Wan, Peng Jun ^a   Yi, Chih Wei ^b  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b NATIONAL CHIAO TUNG UNIVERSITY   (Taiwan)

Author keywords

Asymptotic probability distribution; Gabriel graph; Poisson point process; The longest edge; Topology control; Wireless ad hoc network

Indexed keywords

DATA COMMUNICATION SYSTEMS; GRAPH THEORY; NETWORK PROTOCOLS; POISSON RATIO; PROBABILITY DISTRIBUTIONS;

ASYMPTOTIC PROBABILITY DISTRIBUTION; GABRIEL GRAPH; POISSON POINT PROCESS; TOPOLOGY CONTROL; WIRELESS AD HOC NETWORK;

COMPUTER NETWORKS;

EID: 33845521013     PISSN: 10459219     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPDS.2007.253285     Document Type: Article

References (13)

1. N. Li, J.C. Hou, and L. Sha, "Design and Analysis of a MST-Based Distributed Topology Control Algorithm for Wireless Ad-Hoc Networks," Proc. 22nd Ann. Joint Conf. IEEE Computer and Comm. Soc. (INFOCOM '03), vol. 3, pp. 1702-1712, Apr. 2003.
2. Y. Wang and X.-Y. Li, "Localized Construction of Bounded Degree and Planar Spanner for Wireless Ad Hoc Networks," Proc. 2003 Joint Workshop Foundations of Mobile Computing (DIALM-POMC '03), pp. 59-68, Sept. 2003.
3. J. Cartigny, F. Ingelrest, D. Simplot-Ryl, and I. Stojmenovic, "Localized LMST and RNG Based Minimum-Energy Broadcast Protocols in Ad Hoc Networks," Ad Hoc Networks, vol. 3, no. 1, pp. 1-16, 2004.
4. E.N. Gilbert, "Random Plane Networks," J. Soc. for Industrial and Applied Math., vol. 9, no. 4, pp. 533-543, Dec. 1961.
5. P. Gupta and P.R. Kumar, "Critical Power for Asymptotic Connectivity in Wireless Networks," Stochastic Analysis, Control, Optimization and Applications: A Volume in Honor of W.H. Fleming, W.M. McEneaney, G. Yin, and Q. Zhang, eds., pp. 547-566, Birkhauser, Mar. 1998.
6. H. Dette and N. Henze, "The Limit Distribution of the Largest Nearest-Neighbour Link in the Unit d-Cube," J. Applied Probability, vol. 26, pp. 67-80, 1989.
7. M.D. Penrose, "The Longest Edge of the Random Minimal Spanning Tree," The Annals of Applied Probability, vol. 7, no. 2, pp. 340-361, 1997.
8. G. Kozma, Z. Lotker, M. Sharir, and G. Stupp, "Geometrically Aware Communication in Random Wireless Networks," Proc. 23rd Ann. ACM Symp. Principles of Distributed Computing, pp. 310-319, July 2004.
9. P.-J. Wan and C.-W. Yi, "Asymptotic Critical Transmission Ranges for Connectivity in Wireless Ad Hoc Networks With Bernoulli Nodes," Proc. IEEE Wireless Comm. and Networking Conf. (WCNC '05), Mar. 2005.
10. C.-W. Yi, P.-J. Wan, X.-Y. Li, and O. Frieder, "Asymptotic Distribution of the Number of Isolated Nodes in Wireless Ad Hoc Networks with Bernoulli Nodes," Proc. IEEE Wireless Comm. and Networking Conf. (WCNC '03), Mar. 2003.
11. M. Penrose, Random Geometric Graphs. Oxford Univ. Press, 2003.
12. H. Zhang and J.C. Hou, "On the Critical Total Power for Asymptotic κ-Connectivity in Wireless Networks," Proc. 24th Ann. Joint Conf. IEEE Computer and Comm. Soc. (INFOCOM '05), Mar. 2005.
13. N. Alon and J.H. Spencer, The Probabilistic Method, second ed. Wiley, Mar. 2000.