An optimal algorithm for constructing oriented Voronoi diagrams and geographic neighborhood graphs
Information Processing Letters
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
On the euclidean bottleneck full Steiner tree problem
Proceedings of the twenty-seventh annual symposium on Computational geometry
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Let P and S be two disjoint sets of n and m points in the plane, respectively. We consider the problem of computing a Steiner tree whose Steiner vertices belong to S, in which each point of P is a leaf, and whose longest edge length is minimum. We present an algorithm that computes such a tree in O((n+m)logm) time, improving the previously best result by a logarithmic factor. We also prove a matching lower bound in the algebraic computation tree model.