A lower bound for computing Oja depth

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A lower bound for computing Oja depth

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(n log n) 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 sig...

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ژورنال

عنوان ژورنال: Information Processing Letters

سال: 2005

ISSN: 0020-0190

DOI: 10.1016/j.ipl.2005.05.014