Thresholding random geometric graph properties motivated by ad hoc sensor networks

Journal of Computer and System Sciences

Volumn 76, Issue 7, 2010, Pages 686-696

  Muthukrishnan, S ^a   Pandurangan, Gopal ^b  

^a RUTGERS UNIVERSITY   (United States)

^b Purdue University   (United States)

Author keywords

Connectivity; Coverage; Local algorithm; Random geometric graphs; Sensor network models; Stretch; Thresholds

Indexed keywords

AD HOC NETWORKS; GEOMETRY; GRAPH ALGORITHMS; SENSOR NETWORKS; SOLVENTS; STRETCHING;

CONNECTIVITY; COVERAGE; LOCAL ALGORITHM; RANDOM GEOMETRIC GRAPHS; THRESHOLDS;

GRAPH THEORY;

EID: 77955415628     PISSN: 00220000     EISSN: 10902724     Source Type: Journal    
DOI: 10.1016/j.jcss.2010.01.002     Document Type: Article

References (35)

1. W. Aiello, F. Chung-Graham, and L. Lu Random evolution of massive graphs James Abello, Handbook on Massive Data Sets 2002 Kluwer Academic Publishers 97 122 extended abstract appeared in FOCS, 2001, pp. 510-519
2. N. Alon, and J. Spencer The Probabilistic Method 2000 John Wiley
3. D. Aldous Probability Approximations via the Poisson Clumping Heuristic 1989 Springer-Verlag
4. D. Aldous http://stat-www.berkeley.edu/users/aldous/Networks/ Spring 2003
5. M. Appel, and R. Russo The connectivity of a graph on uniform points on [ 0, 1 ] d Statist. Probab. Lett. 60 2002 351 357
6. M. Appel, and R. Russo The maximum vertex degree of a graph on uniform points in [ 0, 1 ] d Adv. in Appl. Probab. 1997 567 581 (Pubitemid 127539019)
7. M. Appel, and R. Russo The minimum vertex degree of a graph on uniform points in [ 0, 1 ] d Adv. in Appl. Probab. 1997 582 594 (Pubitemid 127539020)
8. B. Bollobas Random Graphs 2001 Cambridge University Press
9. J. Dall, and M. Christensen Random geometric graphs Phys. Rev. E 66 1 2002 016121 9 pp
10. B. Deb, S. Bhatnagar, and B. Nath A topology discovery algorithm for sensor networks with applications to network management Tech. Report DCS-TR 441, Rutgers Univ. athos.rutgers.edu/dataman/papers.html 2002
11. L. Devroye A log log law for maximal uniform spacings Ann. Probab. 26 1982 67 80
12. J. Diaz, J. Petit, and M. Serna Random geometric problems on [ 0, 1 ] 2 Randomization and Approximation Techniques in Computer Science Lecture Notes in Comput. Sci. vol. 1518 1998 294 306
13. J. Diaz, M. Penrose, J. Petit, and M. Serna Linear ordering of random geometric graphs Graph Theoretic Concepts in Computer Science Lecture Notes in Comput. Sci. vol. 1665 1999
14. p metric, in: 12th International Symposium on Graph Drawing, 2004
15. A. Flaxman, A. Frieze, and E. Upfal Efficient communication in an ad-hoc network J. Algorithms 52 2004 1 7
16. D. Ganesan, R. Govindan, S. Shenker, and D. Estrin Highly resilient, energy-efficient multipath routing in wireless sensor networks Mobile Comput. Commun. Rev. 1 2 2002
17. G. Grimmett Percolation 1999 Springer-Verlag
18. A. Goel, S. Rai, B. Krishnamachari, Sharp thresholds for monotone properties for random geometric graphs, in: Proc. of ACM STOC, 2004
19. P. Gupta, and P.R. Kumar Critical power for asymptotic connectivity in wireless networks W.M. McEneaney, G. Yin, Q. Zhang, Stochastic Analysis, Control, Optimization and Applications: A Volume in Honor of W.H. Fleming 1998 Birkhäuser Boston
20. P. Gupta, and P.R. Kumar The capacity of wireless networks IEEE Trans. Inform. Theory 46 2 2000 388 404
21. P. Hall Introduction to the Theory of Coverage Processes 1988 John Wiley
22. P. Jaillet On properties of geometric random graph problems in the plane Ann. Oper. Res. 61 1995 1 20
23. J. Kleinberg, The small-world phenomenon: An algorithmic perspective, in: Proc. 32nd ACM Symposium on Theory of Computing, 2000
24. J. Kleinberg, S.R. Kumar, P. Raghavan, S. Rajagopalan, A. Tomkins, The Web as a graph: Measurements, models and methods. Invited survey at the 5th Annual International Computing and Combinatorics conference (COCOON), 1999
25. B. Krishnamachari, S. Wicker, R. Bejar, and M. Pearlman Critical density thresholds in distributed wireless networks in: Proc. of GLOBECOM, 2001. Enlarged version appeared H. Bhargava, H.V. Poor, V. Tarokh, S. Yoon, Communications, Information and Network Security 2002 Kluwer Publishers
26. S. Meguerdichian, F. Koushanfar, M. Potkonjak, M. Srivastava, Coverage problems in wireless ad-hoc sensor networks, in: Proc. of INFOCOM 2001, pp. 1380-1387
27. R. Meester, and R. Roy Continuum Percolation 1996 Cambridge University Press
28. G. Narasimhan, and M. Smid Approximating the stretch factor of Euclidean graphs SIAM J. Comput. 30 2000 978 989
29. M.D. Penrose Random Geometric Graphs 2003 Oxford University Press
30. M.D. Penrose The longest edge of the random minimal spanning tree Ann. Appl. Probab. 7 1997 340 361
31. M. Penrose On k-connectivity for a geometric random graph Random Structures Algorithms 15 1999 145 164
32. T. Phillips, S. Panwar, and A. Tantawi Connectivity properties of a packet radio network model IEEE Trans. Inform. Theory 35 5 1989 1044 1047
33. P. Piret On the connectivity of radio networks IEEE Trans. Inform. Theory 37 5 1991 1490 1492
34. P. Santi, and D. Blough The critical transmitting range for connectivity in sparse wireless ad hoc networks IEEE Trans. Mobile Comput. 2 1 2003 25 39
35. A. Tsirigos, Z. Haas, S. Tabrizi, Multipath routing in mobile ad hoc networks or how to route in the presence of topological changes, in: IEEE MILCOM, 2001