Slowing down sorting networks to obtain faster sorting algorithms
Journal of the ACM (JACM)
On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
An optimal-time algorithm for slope selection
SIAM Journal on Computing
Fat triangles determine linearly many holes
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Dynamic three-dimensional linear programming
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Computing a segment center for a planar point set
Journal of Algorithms
Geometric algorithms in AdeptRAPID
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Hierarchical vertical decompositions, ray shooting, and circular arc queries in simple polygons
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Faster construction of planar two-centers
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
More planar two-center algorithms
Computational Geometry: Theory and Applications
A simple linear algorithm for computing rectilinear 3-centers
Computational Geometry: Theory and Applications - Special issue: The 11th Candian conference on computational geometry - CCCG 99
New Algorithms for k-Center and Extensions
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
A Scheme for Computing Minimum Covers within Simple Regions
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
A simple linear algorithm for computing rectilinear 3-centers
Computational Geometry: Theory and Applications - Special issue: The 11th Candian conference on computational geometry - CCCG 99
Optimal cover of points by disks in a simple polygon
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Minimal containment under homothetics: a simple cutting plane approach
Computational Optimization and Applications
Optimal Cover of Points by Disks in a Simple Polygon
SIAM Journal on Computing
An approximation algorithm for k-center problem on a convex polygon
Journal of Combinatorial Optimization
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Given a set S of n points in the plane and a set O of pairwise disjoint simple polygons with a total of m edges, we wish to find two congruent disks of smallest radius whose union covers S and whose centers lie outside the polygons in O (referred to as locational constraints in facility location theory). We present an algorithm to solve this problem in randomized expected time O(m log2(mn) + mn log2 n log(mn)). We also present an efficient approximation scheme that constructs, for a given ε 0, two disks as above of radius at most (1 + ε)r*, where r* is the optimal radius, in time O(1/ε log(1/ε)(m log2 m + n log2 n)) or in randomized expected time O(1/ε log(1/ε)((m + n log n) log(mn))).