Opposite-Quadrant Depth in the Plane
نویسندگان
چکیده
منابع مشابه
Opposite-Quadrant Depth in the Plane
Given a set S of n points in the plane, the opposite-quadrant depth of a point p ∈ S is defined as the largest number k such that there are two opposite axis-aligned closed quadrants (NW and SE, or SW and NE) with apex p, each quadrant containing at least k elements of S. We prove that S has a point with opposite-quadrant depth at least n/8. If the elements of S are in convex position, then we ...
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Given a set P of n points in the plane, the Oja-depth of a point x ∈ R is defined to be the sum of the areas of all triangles defined by x and two points from P , normalized by the area of convex-hull of P . The Ojadepth of P is the minimum Oja-depth of any point in R. The Oja-depth conjecture states that any set P of n points in the plane has Oja-depth at most n/9 (this would be optimal as the...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2007
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-007-0707-2