Size and weight of shortest path trees with exponential link weights

Combinatorics Probability and Computing

Volumn 15, Issue 6, 2006, Pages 903-926

  Van Der Hofstad, Remco ^a   Hooghiemstra, Gerard ^b   Van Mieghem, Piet ^b  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b Delft University of Technology ^*  (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTION EVALUATION; GRAPH THEORY; NUMBER THEORY; PROBLEM SOLVING; RECURSIVE FUNCTIONS;

NODES; RECURSIVE TREE; SHORTEST PATH TREE (SPT);

TREES (MATHEMATICS);

EID: 33750331600     PISSN: 09635483     EISSN: 14692163     Source Type: Journal    
DOI: 10.1017/S0963548306007802     Document Type: Article

References (28)

1. Abramowitz, M. and Stegun, I. A. (1968) Handbook of Mathematical Functions, Dover.
2. Bollobás, B. (2001) Random Graphs, 2nd edn, Cambridge University Press.
3. Bollobás, B., Gamarnik, D., Riordan, O. and Sudakov, B. (2004) On the value of a random minimum weight Steiner tree. Combinatorica 24 187-207.
4. Chuang, J. and Sirbu, M. (1998) Pricing multicast communication: A cost-based approach. Telecommunication Systems 17 281-297.
5. Dobrow, R. P. and Smythe, R. T. (1996) Poisson approximations for functionals of random trees. Random Struct. Alg. 9 79-92.
6. Faloutsos, M., Faloutsos, P. and Faloutsos, C. (1999) On power law relations of the internet topology. In Proc. ACM-SIGCOM'99,pp. 251-262.
7. Frieze, A. M. (1985) On the value of a random minimum spanning tree problem. Discrete Appl. Math. 10 47-56.
8. Frieze, A. M. and Grimmett, G. R. (1985) The shortest-path problem for graphs with random arc-lengths. Discrete Appl. Math. 10 57-77.
9. Gradshteyn, I. S. and Ryzhik, I. M. (1994) Table of Integrals, Series and Products, 5th edn, Academic Press.
10. Hassin, R. and Zemel, E. (1985) On shortest paths in graphs with random weights. Math. Oper. Res. 10 557-564.
11. Hekmat, R. and Van Mieghem, P. (2003) Degree distribution and hopcount in wireless ad-hoc networks. In 11th IEEE International Conference on Networks (ICON 2003), pp. 603-609.
12. van der Hofstad, R., Hooghiemstra, G. and Van Mieghem, P. (2001) First-passage percolation on the random graph. Probab. Engrg. Inform. Sci. (PEIS) 15 225-237.
13. van der Hofstad, R., Hooghiemstra, G. and Van Mieghem, P. (2002) The flooding time in random graphs. Extremen 5 111-129.
14. van der Hofstad, R., Hooghiemstra, G. and Van Mieghem, P. (2002) On the covariance of the level sizes in random recursive trees. Random Struct. Alg. 20 519-539.
15. Hwang, F. K., Richards, D. S. and Winter, P. (1992) The Steiner Tree Problem, Vol. 53 of Ann. Discrete Math., North-Holland, Amsterdam.
16. Janic, M. and Van Mieghem, P. (2004) The gain and cost of multicast routing trees.In International Conference on Systems, Man and Cybernetics (IEEE SMC 2004), pp. 4625-4630.
17. Janson, S. (1999) One, two and three times log n/n for paths in a complete graph with random weights. Combin. Probab. Comput. 8 347-361.
18. Karp, R. M. (1975) On the computational complexity of combinatorial problems. Networks 5 45-68.
19. Moon, J. W. (1974) The distance between nodes in recursive trees.In Combinatorics, Vol. 13 of London Math. Soc. Lecture Notes Ser., Cambridge University Press, London, pp. 125-132.
20. Phillips, G., Shenker, S. and Tangmunarunkit, H. (1999) Scaling of multicast trees: Comments on the Chuang-Sirbu scaling law.In Proc. ACM-SIGCOMM'99, pp. 41-51.
21. Riordan, J. (1968) Combinatorial Identities, Wiley.
22. Robinson, S. (2004) The prize of anarchy. SIAM News 37(5) 1-4.
23. Smythe, R. T. and Mahmoud, H. M. (1995) A survey of recursive trees. Theor. Probability and Math. Statist. 51 1-27.
24. Srivastava, H. M. and Choi, J. (2001) Series Associated with the Zeta and Related Functions, Kluwer, Dordrecht.
25. Van Mieghem, P., Hooghiemstra, G. and van der Hofstad, R. A scaling law for the hopcount. Report 2000125:http://www.nas.ewi.tudelft.nl/people/Piet/ teleconference.html
26. Van Mieghem, P., Hooghiemstra, G. and van der Hofstad, R. (2001) On the efficiency of multicast. IEEE/ACM Trans. Networking 9 719-732.
27. Van Mieghem, P. and Janic, M. (2002) Stability of a multicast tree. In Proc. IEEE INFOCOM2002, Vol. 2, pp. 1099-1108.
28. Van Mieghem, P., Kuipers, F. A., Korkmaz, T., Krunz, M., Curado, M., Monteiro, E., Masip-Bruin, X., Solé-Pareta, J. and Sánchez- López, S. (2003) Quality of service routing. Chapter 3 in Quality of Future Internet Services: EU-COST 263 Final Report (Smirnov et al., eds), Vol. 2856 of Lecture Notes in Computer Science, Springer, pp. 80-117.