Weighted Variants of The Problem
The weighted version of the minimum covering circle problem takes as input a set of points in a Euclidean space, each with weights; the goal is to find a single point that minimizes the maximum weighted distance to any point. The original minimum covering circle problem can be recovered by setting all weights to the same number. As with the unweighted problem, the weighted problem may be solved in linear time in any space of bounded dimension, using approaches closely related to bounded dimension linear programming algorithms, although slower algorithms are again frequent in the literature. The weighted version of the Elzinga-Hearn algorithm is available via the ORSEP article mentioned above.
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