Günter Rote:

Computing the minimum Hausdorff distance between two point sets on a line under translation

Information Processing Letters 38 (1991), 123–127, (Zbl 736.68078, MR #92d:68114). doi:10.1016/0020-0190(91)90233-8

Abstract

Given two sets of points on a line, we want to translate one of them so that their Hausdorff distance is minimized. (The Hausdorff distance between two sets the maximum of the distances from a point in any of the two sets to the nearest point in the other set.) We present an optimal O(n log n) algorithm for this problem.
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