Computing a centerpoint of a finite planar set of points in linear time
The notion of a centerpoint of a finite set of points in two and higher dimensions is a generalization of the concept of the median of a set of reals. In this paper we present a linear-time algorithm for computing a centerpoint of a set ofn points in the plane, which is optimal compared with theO(n log3n) complexity of the previously best-known algorithm. We use suitable modifications of the hamsandwich cut algorithm in [Me2] and the prune-and-search technique of Megiddo [Me1] to achieve this improvement.
KeywordsLinear Time Discrete Comput Geom Sorting Network Pairwise Intersection Finite Planar
- [JM]S. Jadhav and A. Mukhopadhyay. Designing optimal geometric algorithms using partial sorting networks. Technical Report TRCS-93-165, Indian Institute of Technology, Kanpur, 1993. Accepted in the Third National Seminar on Theoretical Computer Science, 1993, Kharagpur, India.Google Scholar
- [Ma]J. Matoušek. Approximations and optimal geometric divide-and-conquer.Proc. 23rd Annual ACM Symposium on Theory of Computing, pages 505–511, 1991.Google Scholar
- [T]Shang-Hua Teng. Center Points and Graph Separators. Ph.D. thesis, School of Computer Science, Carnegie-Mellon University, 1993.Google Scholar