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Given a set S of n points in the plane and a constant α, the alpha-connected two-center problem is to find two congruent closed disks of the smallest radius covering S, such that the distance of the two centers is at most 2(1 − α)r. We present an O(n 2 log 2 n) expected-time algorithm for this problem, improving substantially the previous O(n 5)-time(More)
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