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The skyline of a set P of multi-dimensional points (tuples) consists of those points in P for which no clearly better point in P exists, using component-wise comparison on domains of interest. While many algorithms have been proposed for efficient computation of skylines, virtually all of them fail to terminate quickly when the skyline set is large, typically displaying quadratic complexity. Large skyline can occur even if the number of dimensions is low, but where the data set is anti-correlated - a common situation in practice. In this paper we propose a new approach for computing large skylines quickly when the dimensionality is low. We show that for two domains of interest, skyline computation can be performed in linear time (plus near-linear time for index construction if not done beforehand), and that for three dimensions this is possible in near-linear time, regardless of skyline size.