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Consider the problem of finding a point in a unit n-dimensional $$\ell _p$$ ℓp -ball ($$p\ge 2$$ p≥2 ) such that the minimum of the weighted Euclidean distance from given m points is maximized. We show in this paper that the recent SDP-relaxation-based approximation algorithm (Haines et al., SIAM J Optim 23(4):2264–2294, 2013) will not only provide the first theoretical approximation bound of $$\frac{1-O\left(...
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