The maxmin facility location or obnoxious facility location problem seeks a location which maximizes the minimum distance to the sites. In the case of the Euclidean metric, it is known as the largest empty sphere problem. The planar case (largest empty circle problem) may be solved in optimal time
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“In progress of time, when my mind was, as it were, strongly impregnated with the Johnsonian æther, I could, with much more facility and exactness, carry in my memory and commit to paper the exuberant variety of his wit and wisdom.”
—James Boswell (1740–1795)