We consider the planar Euclidean two-center problem in which given n points in the plane  find two congruent disks of the smallest radius covering the points. We present a deterministic O(n \log n)-time algorithm for the case that the centers of the two optimal disks are close together , that is, the overlap of the two optimal disks is a constant fraction of the disk area. This improves the previous best O(n\log n\log\log n) bound by Wang for the case. We also present a deterministic O(n\log n)-time algorithm for the case that the input points are in convex position  .
We consider the planar Euclidean two-center problem in which given n points in the plane we are to find two congruent disks of the smallest radius covering the points. We present a deterministic O(n \log n)-time algorithm for the case that the centers of the two optimal disks are close to each other , that is, the overlap of the two optimal disks is a constant fraction of the disk area. We also present a deterministic O(n\log n)-time algorithm for the case that the input points are in convex position . Both results improve the previous best O(n\log n\log\log n) bound on the problems .
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we are to
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together
to each other
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This improves the previous best O(n\log n\log\log n) bound by Wang for the case.
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. Both results improve the previous best O(n\log n\log\log n) bound on the problems