Steiner Trees, Coordinate Systems and NP-Hardness
Given a set A of points a 1, a 2,..., in the Euclidean plane, the Steiner tree problem asks for a minimum network T(A) (or T if A is not necessarily mentioned) interconnecting A with some additional points to shorten the network . The given points are referred to as terminals and the additional points are referred to as Steiner points. Trivially, T is a tree, called the Euclidean Steiner minimal tree (ESMT) for A. It is well known that Steiner minimal trees satisfy an angle condition: all angles at the vertices of Steiner minimal trees are not less than 120° . A tree satisfying this angle condition is called a Steiner tree. Therefore, a Steiner minimal tree must be a Steiner tree.
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- M. Brazil, D.A. Thomas and J.F. Weng, Gradient-constrained minimal Steiner trees, DIMACS Series in Discrete Math. and Theoretical Comput. Science, Vol. 40, pp. 23–38.Google Scholar
- M. Brazil, D.A. Thomas and J.F. Weng, On the complexity of the Steiner problem, preprint.Google Scholar
- J.F. Weng, Steiner problem in hexagonal metric, unpublished manuscript.Google Scholar
- J.F. Weng, A new model of generalized Steiner trees and 3-coordinate systems, DIMACS Series in Discrete Math. and Theoretical Comput. Science, Vol. 40, pp. 415–424.Google Scholar