Abstract
Given a set S of n points in R 2 , the Oja depth of a point θ is the sum of the areas of all triangles formed by θ and two elements of S. A point in R 2 with minimum depth is an Oja median. We show how an Oja median may be computed in O( nlog 3 n) time. In addition, we present an algorithm for computing the Fermat–Torricelli points of n lines in O( n) time. These points minimize the sum of weighted distances to the lines. Finally, we propose an algorithm which computes the simplicial median of S in O( n 4) time. This median is a point in R 2 which is contained in the most triangles formed by elements of S.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
