Computing the extreme distances between two convex polygons
Journal of Algorithms
Computational geometry: an introduction
Computational geometry: an introduction
Determining the separation of preprocessed polyhedra: a unified approach
Proceedings of the seventeenth international colloquium on Automata, languages and programming
Dynamic three-dimensional linear programming
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
A Simple Primal Algorithm for Intersecting 3-Polyhedra in Linear Time
A Simple Primal Algorithm for Intersecting 3-Polyhedra in Linear Time
CLARANS: A Method for Clustering Objects for Spatial Data Mining
IEEE Transactions on Knowledge and Data Engineering
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This paper gives optimal logarithmic-time algorithms for two problems related to computing vertices of Voronoi diagrams in the plane: 1) given a convex polygon, compute the largest homothet of a given triangle that can be inscribed in the polygon and 2) given three disjoint convex polygons, compute the points that are equidistant from all three. These algorithms are based on a prune-and-search technique that may make tentative discards that are later revoked or certified. In three dimensions, a general strategy using hierarchical data structures leads to poly-logarithmic algorithms for related problems.