Slowing down sorting networks to obtain faster sorting algorithms
Journal of the ACM (JACM)
Optimal point location in a monotone subdivision
SIAM Journal on Computing
On k-hulls and related problems
SIAM Journal on Computing
Lines in space-combinators, algorithms and applications
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
An optimal-time algorithm for slope selection
SIAM Journal on Computing
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Selecting distances in the plane
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Approximations and optimal geometric divide-and-conquer
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Extremal polygon containment problems
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
A singly exponential stratification scheme for real semi-algebraic varieties and its applications
Theoretical Computer Science
Euclidean minimum spanning trees and bichromatic closest pairs
Discrete & Computational Geometry
Randomized optimal algorithm for slope selection
Information Processing Letters
An optimal convex hull algorithm and new results on cuttings (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Ray shooting and parametric search
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Applications of parametric searching in geometric optimization
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Finding the repeated median regression line
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Journal of Algorithms
On the zone of a surface in a hyperplane arrangement
Discrete & Computational Geometry
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Computating the width of a set
SCG '85 Proceedings of the first annual symposium on Computational geometry
Incidence and nearest-neighbor problems for lines in 3-space
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
On lines missing polyhedral sets in 3-space
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Geometric partitioning made easier, even in parallel
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Finding a minimum weight K-link path in graphs with Monge property and applications
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
An expander-based approach to geometric optimization
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Compatible tetrahedralizations
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
A deterministic algorithm for the three-dimensional diameter problem
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Efficient piecewise-linear function approximation using the uniform metric: (preliminary version)
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Efficient randomized algorithms for the repeated median line estimator
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Computing a minimum-weight k-link path in graphs with the concave Monge property
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Using sparsification for parametric minimum spanning tree problems
Nordic Journal of Computing
Incremental Penetration Depth Estimation between Convex Polytopes Using Dual-Space Expansion
IEEE Transactions on Visualization and Computer Graphics
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We apply Megiddo's parametric searching technique to several geometric optimization problems and derive significantly improve solutions for them. We obtain, for any fixed &egr; 0, an O(n1+&egr;) algorithm for computing the diameter of a point set in 3-space, an O(n8/5+&egr;) algorithm for computing the closest pair in a set of n lines in space. All these algorithms are deterministic. We also look at the problem of computing the k-th smallest slope formed by the lines joining n points in the plane. In 1989 Cole, Salowe, Steiger, and Szemere´di gave an optimal but very complicated O(n log n) solution based on Megiddo's technique. We follow a different route and give a very simple O(n log2 n) solution which bypasses parametric searching altogether.