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Publications [#235528] of Pankaj K. Agarwal

Papers Published

  1. Agarwal, PK; Ben-Avraham, R; Sharir, M, The 2-center problem in three dimensions, Proceedings of the Annual Symposium on Computational Geometry (2010), pp. 87-96 [doi]
    (last updated on 2017/12/17)

    Abstract:
    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.

 

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