Covering algorithms, continuum percolation and the geometry of wireless networks

Annals of Applied Probability

Volumn 13, Issue 2, 2003, Pages 722-741

  Booth, Lorna ^a,d   Bruck, Jehoshua ^b   Franceschetti, Massimo ^b   Meester, Ronald ^c  

^a UTRECHT UNIVERSITY   (Netherlands)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^c VU UNIVERSITY AMSTERDAM   (Netherlands)

^d UTRECHT UNIVERSITY   (Netherlands)

Author keywords

(continuum) percolation; Covering algorithms; Phase transition; Wireless communication networks

Indexed keywords

EID: 21144445765     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/aoap/1050689601     Document Type: Article

References (21)

1. AGARWAL, P. J. and SHARIR, M. (1998). Efficient algorithms for geometric optimization. ACM Computing Surveys 30 412-458.
2. BOOTH, L. (2002). Random spatial structures and sums. Ph.D. dissertation, Utrecht Univ.
3. BOOTH, L., BRUCK, J., FRANCESCHETTI, M. and MEESTER, R. (2002). Technical Report ETR037, Caltech. Available at www.paradise.caltech.edu/ETR.html.
4. DURRETT, R. and GRIFFEATH, D. (1983). Supercritical contact processes on ℤ. Ann. Probab. 11 1-15.
5. ERDOS, P. and RÉNYI, A. (1959). On random graphs, I. Publ. Math. Debrecen. 6 290-297.
6. ERDOS, P. and RÉNYI, A. (1960). On the evolution of random graphs. Publ. Math. Inst. Hungarian Acad. Sci. 5 17-61.
7. ERDOS, P. and RÉNYI, A. (1961a). On the evolution of random graphs. Bull. Internat. Inst. Statist. Tokyo 38 343-347.
8. ERDOS, P. and RÉNYI, A. (1961b). On the strength of connectedness of a random graph. Acta Math. Acad. Sci. Hungar. 12 261-267.
9. FRANCESCHETTI, M., COOK, M. and BRUCK, J. (2001). A geometric theorem for approximate disk covering algorithms. Available at www.paradise.caltech.edu/ ETR.html.
10. GERLA, M. and TSAI, J. T. (1995). Multicluster, mobile, multimedia radio network. ACM/Baltzer Wireless Nenorks 1 255-265.
11. GILBERT, E. N. (1961). Random plane networks. SIAM J. 9 533-543.
12. GUPTA, P. and KUMAR, P. R. (1998). Critical power for asymptotic connectivity in wireless networks. In Stochastic Analysis, Control, Optimization and Applications: A Volume in Honor of W. H. Fleming (W. M. McEneany, G. Yin and Q. Zhang, eds.) 547-566. Birkhäuser, Boston.
13. GUPTA, P. and KUMAR, P. R. (2000). The capacity of wireless networks. IEEE Trans. Inform. Theory 46 388-404.
14. HALL, P. (1985). On continuum percolation. Ann. Probab. 13 1250-1266.
15. HALL, P. (1988). Introduction to the Theory of Coverage Processes. Wiley, New York.
16. MEESTER, R. and ROY, R. (1994). Uniqueness of unbounded occupied and vacant components in boolean models. Ann. Appl. Probab. 4 933-951.
17. MEESTER, R. and ROY, R. (1996). Continuum Percolation. Cambridge Univ. Press.
18. MENSHIKOV, M. V. (1986). Coincidence of critical points in percolation problems. Soviet Math. Dokl. 24 856-859.
19. PENROSE, M. (1997). The longest edge of the random minimal spanning tree. Ann. Appl. Probab. 7 340-361.
20. 2. Ann. Probab. 18 1563-1575.
21. YUKICH, J. E. (1998). Probability Theory of Classical Euclidean Optimization Problems. Lecture Notes in Math. 1675. Springer, New York.