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Let S={s1,…,sn} be a set of points in the plane. The Oja depth of a query point θ with respect to S is the sum of the areas of all triangles (θ,si,sj). This depth may be computed in O(nlogn) time in the RAM model of computation. We show that a matching lower bound holds in the algebraic decision tree model. This bound also applies to the computation of the Oja gradient, the Oja sign test, and to the...
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