The 2-center problem in three dimensions


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