论文信息 - The Generation of Minimal Trees with a Steiner Topology

The Generation of Minimal Trees with a Steiner Topology

An iterative method is described which generates a minimal tree with a Steiner topology in at most n 2 steps, where n is the number of fixed vertices. The SI algorithm is formulated. When n < 4, the SI algorithm converges to a proper tree. Experimental studies indicate that this algorithm generates trees close to optimal Steiner minimal trees.

Shi-Kuo Chang | Shi-Kuo Chang

[1] E. Cockayne. On the Steiner Problem , 1967, Canadian Mathematical Bulletin.

[2] E. Cockayne. ON THE EFFICIENCY OF THE ALGORITHM FOR STEINER MINIMAL TREES , 1970 .

[3] E. J. Cockayne. Computation of minimal length full Steiner trees on the vertices of a convex polygon , 1969 .

[4] M. Hanan,et al. On Steiner’s Problem with Rectilinear Distance , 1966 .

[5] F. P. Palermo. A network minimization problem , 1961 .

[6] R. Prim. Shortest connection networks and some generalizations , 1957 .

[7] G. G. Stokes. "J." , 1890, The New Yale Book of Quotations.

[8] H. Coxeter,et al. Introduction to Geometry , 1964, The Mathematical Gazette.

[9] Z. A. Melzak,et al. Steiner’s problem for set-terminals , 1968 .

[10] G. Hardy,et al. What is Mathematics? , 1942, Nature.

[11] E. Gilbert. Minimum cost communication networks , 1967 .

[12] Z. A. Melzak. On the Problem of Steiner , 1961, Canadian Mathematical Bulletin.

[13] Shailendra C. Parikh. Equivalent Stochastic Linear Programs , 1970 .

[14] H. Pollak,et al. Steiner Minimal Trees , 1968 .

[15] Journal of the Association for Computing Machinery , 1961, Nature.