Math @ Duke

Publications [#235528] of Pankaj K. Agarwal
Papers Published
 Agarwal, PK; BenAvraham, R; Sharir, M, The 2center problem in three dimensions,
Proceedings of the Annual Symposium on Computational Geometry
(2010),
pp. 8796 [doi]
(last updated on 2017/12/17)
Abstract: Let P be a set of n points in ℝ3. The 2center 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 2center of P. The first algorithm runs in O(n3 log8 n) expected time, and the second algorithm runs in O(n2 log8 n/(1r*/r 0)3) expected time, where r* is the radius of the 2center 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 2center of P not being very close to each other.


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