کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
10327385 681008 2014 7 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A proof of the Oja depth conjecture in the plane
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
A proof of the Oja depth conjecture in the plane
چکیده انگلیسی
Given a set P of n points in the plane, the Oja depth of a point x∈R2 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 R2. The Oja depth conjecture states that any set P of n points in the plane has Oja depth at most n2/9. 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 Rd, d⩾3, via a different, more combinatorial technique.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computational Geometry - Volume 47, Issue 6, August 2014, Pages 668-674
نویسندگان
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