A very strong zero-one law for connectivity in one-dimensional geometric random graphs

IEEE Communications Letters

Volumn 11, Issue 1, 2007, Pages 55-57

  Han, Guang ^a   Makowski, Armand M ^a  

^a UNIVERSITY OF MARYLAND   (United States)

Author keywords

Connectivity; One dimension wireless networks; Zero one laws

Indexed keywords

COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; GRAPH THEORY; RANDOM PROCESSES;

GEOMETRIC RANDOM GRAPHS; GRAPH CONNECTIVITY; ONE-DIMENSION WIRELESS NETWORKS; ZERO-ONE LAWS;

WIRELESS NETWORKS;

EID: 33947668433     PISSN: 10897798     EISSN: None     Source Type: Journal    
DOI: 10.1109/LCOMM.2007.061142     Document Type: Article

References (15)

1. d," Statistics & Probability Lett., vol. 60, pp. 351-357, 2002.
2. H. A. David and H. N. Nagaraja, Order Statistics, Third Edition. Wiley Series in Probability and Statistics, John Wiley & Sons, 2003.
3. M. Desai and D. Manjunath, "On the connectivity in finite ad hoc networks," IEEE Commun. Lett., vol. 6, pp. 437-439, 2002.
4. L. Devroye, "Laws of the iterated logarithm for order statistics of uniform spacings," The Annals of Probability, vol. 9, pp. 860-867, 1981.
5. C. H. Foh and B. S. Lee, "A closed form network connectivity formula for one-dimensional MANETs," in Proc. 2004 IEEE International Conference on Communications (ICC 2004).
6. C. H. Foh, G. Liu, B. S. Lee, B.-C. Seet, K.-J. Wong, and C. P. Fu, "Network connectivity of one-dimensional MANETs with random waypoint movement," IEEE Commun. Lett., vol. 9, pp. 31-33, 2005.
7. A. Ghasemi and S. Nader-Esfahani, "Exact probability of connectivity in one-dimensional ad hoc wireless networks," IEEE Commun. Lett., vol. 10, pp. 251-253, 2006.
8. E. Godehardt and J. Jaworski, "On the connectivity of a random interval graph," Random Structures and Algorithms, vol. 9, pp. 137-161, 1996.
9. A. D. Gore, "Comments on "On the connectivity in finite ad hoc networks"," IEEE Commun. Lett. vol. 10, pp. 88-90, 2006.
10. P. Gupta and P. R. Kumar, "Critical power for asymptotic connectivity in wireless networks," chapter in Analysis, Control, Optimization and Applications: A Volume in Honor of W. H. Fleming, edited by W. M. McEneany, G. Yin, and Q. Zhang. Boston: Birkhäuser, 1998.
11. G. Han and A. M. Makowski, "Very sharp transitions in one-dimensional MANETs," in Proc. International Conference on Communications (ICC 2006).
12. S. Janson, T. Łuczak, and A. Ruciński, Random Graphs, Wiley-Interscience Series in Discrete Mathematics and Optimization, John Wiley & Sons, 2000.
13. J. Li, L. L. H. Andrew, C. H. Foh, M. Zukerman, and M. Neuts, "Meeting connectivity requirements in a wireless multihop network," IEEE Commun. Lett., vol. 10, pp. 19-21, 2006.
14. G. L. McColm, "Threshold functions for random graphs on a line segment," Combinatorics, Probability and Computing, vol. 13, pp. 373-387, 2004.
15. S. Muthukrishnan and G. Pandurangan, "The bin-covering technique for thresholding random geometric graph properties," in Proc. 16th ACM-SIAM Symposium on Discrete Algorithms (SODA 2005).