Planar point location using persistent search trees
Communications of the ACM
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
On the complexity of some geometric problems in unbounded dimension
Journal of Symbolic Computation
Journal of Algorithms
Journal of Algorithms
Cutting hyperplanes for divide-and-conquer
Discrete & Computational Geometry
Las Vegas algorithms for linear and integer programming when the dimension is small
Journal of the ACM (JACM)
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
On linear-time deterministic algorithms for optimization problems in fixed dimension
Journal of Algorithms
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Faster construction of planar two-centers
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
More planar two-center algorithms
Computational Geometry: Theory and Applications
Vertical Decomposition of Shallow Levels in 3-Dimensional Arrangements and Its Applications
SIAM Journal on Computing
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Linear Programming - Randomization and Abstract Frameworks
STACS '96 Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science
An optimal randomized algorithm for maximum Tukey depth
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
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Let P be a set of n points in R^3. The 2-center problem for P is to find two congruent balls of minimum radius whose union covers P. We present a randomized algorithm for computing a 2-center of P that runs in O(@b(r^@?)n^2log^4nloglogn) expected time; here @b(r)=1/(1-r/r"0)^3, r^@? is the radius of the 2-center balls of P, and r"0 is the radius of the smallest enclosing ball of P. The algorithm is near quadratic as long as r^@? is not too close to r"0, which is equivalent to the condition that the centers of the two covering balls be not too close to each other. This improves an earlier slightly super-cubic algorithm of Agarwal, Efrat, and Sharir (2000) [2] (at the cost of making the algorithm performance depend on the center separation of the covering balls).