Computational geometry: an introduction
Computational geometry: an introduction
Bottleneck Steiner Trees in the Plane
IEEE Transactions on Computers
An approximation algorithm for a bottleneck k-Steiner tree problem in the Euclidean plane
Information Processing Letters
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Approximation algorithm for bottleneck steiner tree problem in the euclidean plane
Journal of Computer Science and Technology
Optimal and approximate bottleneck Steiner trees
Operations Research Letters
Exact Algorithms for the Bottleneck Steiner Tree Problem
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
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We study the Euclidean bottleneck Steiner tree problem: given a set P of n points in the Euclidean plane, called terminals, find a Steiner tree with at most k Steiner points such that the length of the longest edge in the tree is minimized. This problem is known to be NP-hard even to approximate within ratio $\sqrt{2}$. We focus on finding exact solutions to the problem for a small constant k . Based on geometric properties of optimal location of Steiner points, we present an O (n logn ) time exact algorithm for k = 1 and an O (n 2) time algorithm for k = 2. Also, we present an O (n logn ) time exact algorithm to the problem for a special case where there is no edge between Steiner points.