Computational geometry: an introduction
Computational geometry: an introduction
Algorithms for diametral pairs and convex hulls that are optimal, randomized, and incremental
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Farthest neighbors, maximum spanning trees and related problems in higher dimensions
Computational Geometry: Theory and Applications
The Voronoi diagram of curved objects
Proceedings of the eleventh annual symposium on Computational geometry
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Placing two disks in a convex polygon
Information Processing Letters
Algorithms for Packing Two Circles in a Convex Polygon
JCDCG '98 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
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We consider the following problem. Given a polygon P, possibly with holes, and having n vertices, compute a pair of equal radius disks that do not intersect each other, are contained in P, and whose radius is maximized. Our main result is a simple randomized algorithm whose expected running time, on worst case input, is O(n log n). This is optimal in the algebraic decision tree model of computation.