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We consider the problem of deciding if a set of points can be covered by two discs with centers p and q and common radius r such that the ratio d(p; q)=r is bounded below by a user supplied constant. We also present an O(n 2 log 2 n) algorithm for this problem.

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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