Zero-one laws for connectivity in random key graphs

IEEE Transactions on Information Theory

Volumn 58, Issue 5, 2012, Pages 2983-2999

  Yaǧan, Osman ^a,b   Makowski, Armand M ^a  

^a UNIVERSITY OF MARYLAND   (United States)

^b CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Graph connectivity; key predistribution; random key graphs; wireless sensor networks (WSNs); zero one laws

Indexed keywords

GRAPH CONNECTIVITY; KEY PRE-DISTRIBUTION; RANDOM KEY GRAPHS; WIRELESS SENSOR NETWORK (WSNS); ZERO-ONE LAW;

WIRELESS SENSOR NETWORKS;

GRAPH THEORY;

EID: 84860251684     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2011.2181331     Document Type: Conference Paper

References (27)

1. S. R. Blackburn and S. Gerke, "Connectivity of the uniform random intersection graph," Discr. Math., vol. 309, pp. 5130-5140, 2009.
2. B. Bollobás, "Random Graphs," in Cambridge Studies in Advanced Mathematics, 2nd ed. Cambridge, U.K.: Cambridge Univ. Press, 2001.
3. A. Cayley, "A theorem on trees," Q. J. Math., vol. 23, pp. 376-378, 1889.
4. F. Chung and L. Lu, "The diameter of sparse random graphs," Adv. Appl. Math., vol. 26, pp. 257-279, 2001.
5. R. Di Pietro, L. V. Mancini, A. Mei, A. Panconesi, and J. Radhakrishnan, "Sensor networks that are provably secure," presented at the Proc. 2nd IEEE/CreateNet Int. Conf. Security and Privacy in Communication Network, Baltimore, MD, Aug. 2006.
6. R. Di Pietro, L. V. Mancini, A. Mei, A. Panconesi, and J. Radhakrishnan, "Redoubtable sensor networks," ACM Trans. Inf. Syst. Security, vol. TISSEC 11, pp. 1-22, 2008.
7. M. Draief and L. Massoulié, Epidemics and Rumours in Complex Networks, ser. LondonMathematical Society LectureNotes. Cambridge, U.K.: Cambridge Univ. Press, 2010, vol. 369.
8. L. Eschenauer and V. D. Gligor, "A key-management scheme for distributed sensor networks," in Proc. 9th ACM Conf. Comput. Commun. Security, Washington, DC, Nov. 2002, pp. 41-47.
9. E. Godehardt and J. Jaworski, "Two models of random intersection graphs for classification," in Studies in Classification, Data Analysis and Knowledge Organization, O. Optiz and M. Schwaiger, Eds. Berlin, Germany: Springer-Verlag, 2003, vol. 22, pp. 67-82.
10. E. Godehardt, J. Jaworski, and K. Rybarczyk, "Random intersection graphs and classification," in Studies in Classification, Data Analysis and Knowledge Organization, H. Lens and R. Decker, Eds. Berlin, Germany: Springer-Verlag, 2007, vol. 33, pp. 67-74.
11. S. Janson, T. Luczak, and A. Rucinski, Random Graphs, Wiley-Interscience Series in DiscreteMathematics and Optimization. NewYork: Wiley, 2000.
12. M. K. Karonski, E. R. Scheinerman, and K. B. Singer-Cohen, "On random intersection graphs: The subgraph problem," Combin., Probabil. Comput., vol. 8, pp. 131-159, 1999.
13. P. Marbach, "Alower-bound on the number of rankings required in recommender systems using collaborative filtering," in Proc. 42nd Annu. Conf. Inf. Sci. Syst., Princeton, NJ, Mar. 2008, pp. 292-297.
14. G. E. Martin, Counting: The Art of Enumerative Combinatorics. New York: Springer Verlag, 2001.
15. A. Perrig, J. Stankovic, and D. Wagner, "Security in wireless sensor networks," Commun. ACM, vol. 47, pp. 53-57, 2004.
16. K. Rybarczyk, "Diameter of the uniform random intersection graph with a note on the connectivity and the phase transition," Discr. Math., vol. 311, pp. 1998-2019, 2011.
17. K. B. Singer, "Random Intersection Graphs," Ph.D. dissertation, Dept. Math. Sci., Johns Hopkins Univ., Baltimore, MD, 1995.
18. J. Spencer, "Nine lectures on random graphs," in Ecole d'Eté de Probabilités de Saint Flour XXI-1991, ser. Lecture Notes in Mathematics, P. Hennequin, Ed. Berlin, Germany: Springer-Verlag, 1993, vol. 1541, pp. 293-347.
19. D.-M. Sun and B. He, "Review of key management mechanisms in wireless sensor networks," Acta Autom. Sinica, vol. 12, pp. 900-906, 2006.
20. Y. Wang, G. Attebury, and B. Ramamurthy, "A survey of security issues in wireless sensor networks," IEEE Commun. Surv. Tutorials, vol. 8, no. 2, pp. 2-23, Second Quarter 2006.
21. O. Yagan and A. M. Makowski, "On the random graph induced by a random key predistribution scheme under full visibility," in Proc. IEEE Int. Symp. Inf. Theory, Toronto, ON, Jun. 2008, pp. 544-548.
22. O. Yagan and A. M. Makowski, Zero-one laws for connectivity in random key graphs, ISR Tech. Rep. 2009-1 Institute for Systems Research, Univ. Maryland, College Park, 2009.
23. O. Yagan and A. M. Makowski, "Connectivity results for random key graphs," in Proc. IEEE Int. Symp. Inf. Theory, Seoul, Korea, Jun. 2009, pp. 2403-2407.
24. O. Yagan and A. M. Makowski, "On the existence of triangles in random key graphs," in Proc. 47th Annu. Allerton Conf. Commun., Control, Comput., Monticello, IL, Sep. 2009, pp. 1567-1574.
25. O. Yagan and A. M. Makowski, "Connectivity in random graphs induced by a key predistribution scheme: Small key pools," in Proc. 44th Annu. Conf. Inf. Sci. Syst., Princeton, NJ, Mar. 2010, pp. 1-6.
26. O. Yagan and A. M. Makowski, A Zero-One Law for the Existence of Triangles in Random Key Graphs [Online]. Available: http://hdl.handle.net/1903/ 9403 (Original version) and http://hdl.handle.net/1903/1215 (Revised version
27. O. Yagan, "Random Graph Modeling of Key Distribution Schemes in Wireless Sensor Networks," Ph.D. dissertation, Dept. Elect. Comput. Eng., Univ. Maryland, College Park, MD, 2011.