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Article Dans Une Revue Computational Geometry: Theory and Applications Computational Geometry @ ScienceDirect Année : 2014

A Proof of the Oja Depth Conjecture in the Plane

Résumé

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.
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Dates et versions

hal-01026341 , version 1 (21-07-2014)

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  • HAL Id : hal-01026341 , version 1

Citer

Nabil Mustafa, Hans Raj Tiwary, Daniel Werner. A Proof of the Oja Depth Conjecture in the Plane. Computational Geometry: Theory and Applications Computational Geometry @ ScienceDirect, 2014, 47 (6), pp.668-674. ⟨hal-01026341⟩
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