2010/12/13 by Pankaj K. Agarwal, Rinat Ben Avraham, Agarwal, Pankaj K. +3
Business, Management and Accounting · Computer Science · Mathematics · #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #F.2.2 #FOS: Computer and information sciences #Facility Location and Emergency Management #I.5.3 #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1012.2694
openalex publication_date 2010/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let P be a set of n points in R3. The 2-center problem for P is to find two congruent balls of minimum radius whose union covers P. We present two randomized algorithms for computing a 2-center of P. The first algorithm runs in O(n3 log5 n) expected time, and the second algorithm runs in O((n2 log5 n) /(1-r*/r0)3) expected time, where r* is the radius of the 2-center balls of P and r0 is the radius of the smallest enclosing ball of P. The second algorithm is faster than the first one as long as r* is not too close to r0, which is equivalent to the condition that the centers of the two covering balls be not too close to each other.