A Proof of the Oja Depth Conjecture in the PlaneReport as inadecuate




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1 LIGM - Laboratoire d-Informatique Gaspard-Monge 2 Charles University Prague 3 Freie Universität Berlin Berlin

Abstract : Given a set P of n points in the plane, the Oja depth of a point x is defined to be the sum of the areas of all triangles defined by x and two points from P, normalized with respect to the area of the convex hull of P. The Oja depth of P is the minimum Oja depth of any point in the plane. The Oja depth conjecture states that any set P of n points in the plane has Oja depth at most n^2-9. This bound would be tight as there are examples where it is not possible to do better. We present a proof of this conjecture. We also improve the previously best bounds for all \Re^d, d \geq 3, via a different, more combinatorial technique.

Keywords : Statistical data depth Oja depth algorithms





Author: Nabil Mustafa - Hans Raj Tiwary - Daniel Werner -

Source: https://hal.archives-ouvertes.fr/



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