Points with large quadrant-depth

We characterize the set of all pairs (a, b) such that for every set P of n points in general position in R2 there always exists a point p ∈ P and two opposite quadrants determined by the axes-parallel lines through p such that one quadrant contains at least an points of P and the other quadrant contains at least bn points of P. We consider also some generalizations of this problem in the plane and in higher dimensions.

• Type: Conference
• Year: 2010
• Where: COMPGEOM
• Authors: Roel Apfelbaum, Itay Ben-Dan, Stefan Felsner, Rom Pinchasi, Tillmann Miltzow
• Keywords: COMPGEOM 2010, General Position, Opposite Quadrants, Quadrant Contains