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 3n) 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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 69-79 |
| Number of pages | 11 |
| Journal | Computational Geometry: Theory and Applications |
| Volume | 26 |
| Issue number | 1 |
| DOIs | |
| State | Published - Aug 2003 |
Keywords
- Algorithms
- Computational geometry
- Estimators of location
- Fermat-Torricelli problem
- Geometric medians
- Oja depth
- Simplicial depth
ASJC Scopus subject areas
- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics