A Fast Selection Algorithm and the Problem of Optimum Distribution of Effort
Journal of the ACM (JACM)
Convex hulls of finite sets of points in two and three dimensions
Communications of the ACM
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Divide-and-conquer in multidimensional space
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
Binary partitions with applications to hidden surface removal and solid modelling
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Selecting distances in the plane
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Enumerating k distances for n points in the plane
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Finding k farthest pairs and k closest/farthest bichromatic pairs for points in the plane
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
On some geometric selection and optimization problems via sorted matrices
Computational Geometry: Theory and Applications
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Given a finite point-set S in E2, how hard is it to compute the &kgr;th largest interdistance, or say, the &kgr;th largest slope or &kgr;th largest triangular area formed by points of S? We examine the complexity of a general class of problems built from these examples, and present a number of techniques for deriving nontrivial upper bounds. Surprisingly, these bounds often match or come very close to the complexity of the corresponding extremal problems (e.g. computing the largest or smallest interdistance, slope, etc.)