Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Journal of Algorithms
A simple algorithm for determining the envelope of a set of lines
Information Processing Letters
An expander-based approach to geometric optimization
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
A near-linear algorithm for the planar 2-center problem
Proceedings of the twelfth annual symposium on Computational geometry
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Faster construction of planar two-centers
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Mobile facility location (extended abstract)
DIALM '00 Proceedings of the 4th international workshop on Discrete algorithms and methods for mobile computing and communications
A fast algorithm for the alpha-connected two-center decision problem
Information Processing Letters
Rectilinear Static and Dynamic Discrete 2-center Problems
WADS '99 Proceedings of the 6th International Workshop 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
Competitive algorithms for maintaining a mobile center
Mobile Networks and Applications
New Algorithms for k-Center and Extensions
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization 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
The 2-center problem in three dimensions
Proceedings of the twenty-sixth annual symposium on Computational geometry
Minimum-sum dipolar spanning tree in R3
Computational Geometry: Theory and Applications
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We present a new algorithm for the two-center problem: “Given a set S of n points in the real plane, find two closed discs whose union contains all of the points and the radius of the larger disc is minimized.” An almost quadratic O(n2logn) solution is given. The previously best known algorithms for the two-center problem have time complexity O(n2log3n). The solution is based on a new geometric characterization of the optimal discs and on a searching scheme with so-called lazy evaluation. The algorithm is simple and does not assume general position of the input points. The importance of the problem is known in various practical applications including transportation, station placement, and facility location.