The Generation of Minimal Trees with a Steiner Topology

Shi-Kuo Chang
1972 Journal of the ACM  
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. KEY WORDS AND PHRASES: shortest connection network, minimal spanning tree, Steiner minimal tree. CR CATEGORY NUMBERS: 3.57, 3.81, 5.32 In this paper an
more » ... 2 In this paper an iterative procedure is described which can be applied to a minimal tree to construct a better tree having certain desirable properties. Experimental studies indicate that this algorithm, called the SI algorithm in this paper, generates trees close to optimal Steiner minimal trees. Pl: O_< m_< n-2; P2: T is non-self-intersecting; P3: Each A;, 1 < i < n, has at most three incident lines; P4: Each Sj, 1 < j < m, has exactly three incident lines; P5: Each Sj, 1 _< j _< m, is the Steiner point of the triangle formed by the points which directly connect S~ in the tree T. A proper tree T is shown in Figure 2 (a). A tree T' having the same topology as T
doi:10.1145/321724.321733 fatcat:wba5yb4akrep3pba47m52jzm2m