The distribution of node degree in maximum spanning trees

Journal of Statistical Computation and Simulation

Volumn 72, Issue 2, 2002, Pages 101-106

  Willemain, Thomas R ^a   Bennett, Mihoko V ^b  

^a RENSSELAER POLYTECHNIC INSTITUTE   (United States)

^b ZS Associates   (United States)

Author keywords

Maximum spanning tree; Minimum spanning tree; Monte Carlo simulation; Outlier; Random number generation

Indexed keywords

EID: 0036288947     PISSN: 00949655     EISSN: None     Source Type: Journal    
DOI: 10.1080/00949650212139     Document Type: Article

References (21)

1. Adami, C. and Mazure, A. (1999). The use of minimal spanning trees to characterize the 2d cluster galaxy distribution. Astronomy & Astrophysics Supplement Series, 134, 393-400.
2. Aldous, D. (1990). A random tree model associated with random graphs. Random Structures and Algorithms, 1, 383-402.
3. Aldous, D. and Steele, J.M. (1992). Asymptotics for Euclidean minimal spanning trees on random points. Probability Theory and Related Fields, 92, 247-258.
4. Agrawal, P. K., Matousek, J. and Suri, S. (1992). Farthest neighbors, maximum spanning trees and related problems in higher dimensions, Computational Geometry 13, 189-201.
5. Barabasi, A. and Albert, R. (1999). Emergence of scaling in random networks. Science, 28, 509-512.
6. Bennett, M.V. (1999). Application of graph theoretic methods to analysis of high-dimensional data sets, unpublished doctoral dissertation. Department of Decision Sciences and Engineering Systems, Rensselaer Polytechnic Institute, Troy, NY.
7. Bhaskar, G. and Narendran, T.T. (1996). Grouping PCBs for set-up reduction: A maximum spanning tree approach. International Journal of Production Research, 34, 621-632.
8. Chaudhuri, B.B., Rodenacker, K. and Burger, G. (1988). Characterization and featuring of histological section images. Pattern Recognition Letters, 7, 245-252.
9. Faloutsos, M., Faloutsos, P. and Faloutsos, C. (1999). On power-law relationships of the internet topology. Computer Communications Review, 29, 251-262.
10. Friedman, J.H. and Rafsky, L.C. (1979). Multivariate generalizations of the Wald-Wolfowitz and Smirnov two-sample tests. The Annals of Statistics, 7, 697-717.
11. Hilbert, D. and Cohn-Vossen, S. (1952). Geometry and the Imagination (Chelsea, New York).
12. Kruskal, J.B. (1956). On the shortest spanning subtree of a graph and a traveling salesman problem. Proceedings of the American Mathematical Society, 7, 48-50.
13. Ouveysi, I. and Wirth, A. (1999). On design of a survivable network architecture for dynamic routing: Optimal solution strategy and an efficient heuristic. European Journal of Operational Research, 117, 30-44.
14. Penrose, M.D. (1996). The random minimal spanning tree in high dimensions. The Annals of Probability, 24, 1903-1925.
15. Penrose, M.D. (1997). The longest edge of the random minimal spanning tree. The Annals of Applied Probability, 7, 340-361.
16. Penrose, M.D. (1998). Extremes for the minimal spanning tree on normally distributed points. Advances in Applied Probability, 30, 628-639.
17. Reka, A., Jeong, H. and Barabasi, A.-L. (1999). Diameter of the World Wide Web. Nature, 401, 130-131.
18. Robins, G. and Salowe, J.S. (1994). On the maximum degree of minimum spanning trees. In Proceedings of the Annual Symposium on Computational Geometry, 250-258.
19. Steele, J.M., Shepp, L.A. and Eddy, W.F. (1987). On the number of leaves of a Euclidean minimal spanning tree. Journal of Applied Probability, 24, 809-826.
20. Wallet, F. and Dussert, C. (1997). Multifactorial comparative study of spatial point pattern analysis methods. Journal of Theoretical Biology, 187, 437-447.
21. Zahn, C.T. (1971). Graph-theoretical methods for detecting and describing gestalt clusters. IEEE Transactions on Computers, C-20, 68-86.