# The 2-center problem in three dimensions

Published

Journal Article

Let P be a set of n points in ℝ3. The 2-center problem for P is to find two congruent balls of the 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 log8 n) expected time, and the second algorithm runs in O(n2 log8 n/(1-r*/r 0)3) expected time, where r* is the radius of the 2-center 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 very close to r0, which is equivalent to the condition of the centers of the two balls in the 2-center of P not being very close to each other.

### Full Text

### Duke Authors

### Cited Authors

- Agarwal, PK; Ben-Avraham, R; Sharir, M

### Published Date

- July 30, 2010

### Published In

- Proceedings of the Annual Symposium on Computational Geometry

### Start / End Page

- 87 - 96

### Digital Object Identifier (DOI)

- 10.1145/1810959.1810974

### Citation Source

- Scopus