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APPROXIMATING CENTER POINTS WITH ITERATIVE RADON POINTS
1996
International journal of computational geometry and applications
We give a practical and provably good Monte Carlo algorithm for approximating center points. Let P be a set of n points in IR d . A point c ∈ IR d is a β-center point of P if every closed halfspace containing c contains at least βn points of P . Every point set has a 1/(d + 1)-center point; our algorithm finds an Ω(1/d 2 )-center point with high probability. Our algorithm has a small constant factor and is the first approximate center point algorithm whose complexity is subexponential in d.
doi:10.1142/s021819599600023x
fatcat:tp4mz4vz2bf6rf2oujhinqxnfi