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
Rectilinear Static and Dynamic Discrete 2-center Problems
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
Voronoi Diagram for services neighboring a highway
Information Processing Letters
Optimal location of transportation devices
Computational Geometry: Theory and Applications
Optimal Insertion of a Segment Highway in a City Metric
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
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We study a class of geometric optimization problems closely related to the 2-center problem: Given a set S of n pairs of points, assign to each point a color ("red" or "blue") so that each pair's points are assigned different colors and a function of the radii of the minimum enclosing balls of the red points and the blue points, respectively, is optimized. In particular, we consider the problems of minimizing the maximum and minimizing the sum of the two radii. For each case, minmax and minsum, we consider distances measured in the L2 and in the L∞ metrics. Our problems are motivated by a facility location problem in transportation system design, in which we are given origin/destination pairs of points for desired travel, and our goal is to locate an optimal road/flight segment in order to minimize the travel to/from the endpoints of the segment.