Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
L-infinity interdistance selection by parametric search
Information Processing Letters
Journal of Algorithms
Optimal algorithms for tree partitioning
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
An expander-based approach to geometric optimization
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Selection and sorting in totally monotone arrays
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
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
New techniques for computing order statistics in Euclidean space (extended abstract)
SCG '85 Proceedings of the first annual symposium on Computational geometry
The Two-Line Center Problem from a Polar View: A New Algorithm and Data Structure
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
Improved algorithms in geometric optimization via expanders
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
Journal of Computer and System Sciences
Covering a set of points in a plane using two parallel rectangles
Information Processing Letters
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In this paper we apply the selection and optimization technique of Frederickson and Johnson to a number of geometric selection and optimization problems, some of which have previously been solved by parametric search, and provide efficient and simple algorithms. Our technique improves the solutions obtained by parametric search by a log n factor. For example, we apply the technique to the two-line center problem, where we want to find two strips that cover a given set S of n points in the plane, so as to minimize the width of the largest of the two strips.