Computational geometry: an introduction
Computational geometry: an introduction
Bottleneck Steiner Trees in the Plane
IEEE Transactions on Computers
Introduction to Algorithms
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
Exact Algorithms for the Bottleneck Steiner Tree Problem
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
On the euclidean bottleneck full Steiner tree problem
Proceedings of the twenty-seventh annual symposium on Computational geometry
The euclidean bottleneck steiner path problem
Proceedings of the twenty-seventh annual symposium on Computational geometry
The bottleneck 2-connected k-Steiner network problem for k≤2
Discrete Applied Mathematics
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We study the Euclidean bottleneck Steiner tree problem: given a set P of n points in the Euclidean plane and a positive integer k, 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 2 and there was no known exact algorithm even for k=1 prior to this work. In this paper, 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 optimal @Q(nlogn)-time exact algorithm for k=1 and an O(n^2)-time algorithm for k=2. Also, we present an optimal @Q(nlogn)-time exact algorithm for any constant k for a special case where there is no edge between Steiner points.