A note on relative neighborhood graphs
SCG '87 Proceedings of the third annual symposium on Computational geometry
Minimum-weight two-connected spanning networks
Mathematical Programming: Series A and B
Bottleneck Steiner Trees in the Plane
IEEE Transactions on Computers
Solving the Euclidean bottleneck biconnected edge subgraph problem by 2-relative neighborhood graphs
Discrete Applied Mathematics
A fast and simple algorithm for the bottleneck biconnected spanning subgraph problem
Information Processing Letters
A linear time algorithm for the bottleneck biconnected spanning subgraph problem
Information Processing Letters
Exact Algorithms for the Bottleneck Steiner Tree Problem
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
On exact solutions to the Euclidean bottleneck Steiner tree problem
Information Processing Letters
Guaranteed performance heuristics for the bottleneck travelling salesman problem
Operations Research Letters
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The geometric bottleneck Steiner network problem on a set of vertices X embedded in a normed plane requires one to construct a graph G spanning X and a variable set of k=0 additional points, such that the length of the longest edge is minimised. If no other constraints are placed on G, then a solution always exists which is a tree. In this paper, we consider the Euclidean bottleneck Steiner network problem for k@?2, where G is constrained to be 2-connected. By taking advantage of relative neighbourhood graphs, Voronoi diagrams, and the tree structure of block cut-vertex decompositions of graphs, we produce exact algorithms of complexity O(n^2) and O(n^2logn) for the cases k=1 and k=2 respectively. Our algorithms can also be extended to other norms such as the L"p planes.