Title of article :
On The Spread of a Uniformly Distributed Point Set
Author/Authors :
Iranfar , Behnam Combinatorial and Geometric Algorithms Lab - Department of Mathematical Sciences - Yazd University - Yazd, Iran , Farshi , Mohammad Combinatorial and Geometric Algorithms Lab - Department of Mathematical Sciences - Yazd University - Yazd, Iran , Mesrikhani , Amir Combinatorial and Geometric Algorithms Lab - Department of Mathematical Sciences - Yazd University - Yazd, Iran
Abstract :
Let P be a set of n points in ℝd, where d is a constant. The spread (or aspect ratio) of P is the ratio of the distance between the farthest pair of
points in P to the distance between the closest pair of points in P. This ratio is an essential factor that appears in many geometric problems. In
this paper, we show that the expected value of the spread of a set of n uniformly distributed point sets is Θ(n2/d)
Keywords :
expected value , uniform distribution , spread
Journal title :
The CSI Journal on Computer Science and Engineering (JCSE)
