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Given two point sets in the plane, we study the minimization of the (lexiocographic) bottleneck distance between the smaller set and an equally-sized subset of the larger set under translations. We relate this problem to two Voronoi-type diagrams, which are of interest for related problems. Their complexity is shown to be polynomial in the sizes of the sets and algorithms for their construction are given.doi:10.1016/j.comgeo.2015.10.001 fatcat:xhwql2i2sfbwtg6yurrsreuofq