The projection median of a set of points in Rd

The projection median of a finite set of points in R2 was introduced by Durocher and Kirkpatrick [5]. They proved the projection median in R2 provides a better approximation of the 2-dimensional Euclidean median, while maintaining a fixed degree of stability, than other standard estimators, like the center of mass or the rectilinear median. In this paper we study the projection median of a set of points in Rd for d 3. We prove new bounds on the approximation factor and stability of the projection median in Rd , which show that the d-dimensional projection median also maintains a fixed degree of stability and provides a better approximation of the d-dimensional Euclidean median than the d-dimensional rectilinear median. For the special case of d = 3, our results imply that the 3-dimensional projection median is a (3/2)-approximation of the 3dimensional Euclidean median, which settles a conjecture posed by Durocher [4].

• Type: Conference
• Year: 2010
• Where: CCCG
• Authors: Riddhipratim Basu, Bhaswar Bhattacharya, Tanmoy Talukdar
• Keywords: CCCG 2010, Computational Geometry, Euclidean Median, Projection Median, Rectilinear Median