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We consider the classic 1-center problem: Given a set P of n points in a metric space find the point in P that minimizes the maximum distance to the other points of P. We study the complexity of this problem in d-dimensional ℓ_p-metrics and in edit and Ulam metrics over strings of length d. Our results for the 1-center problem may be classified based on d as follows. ∙ Small d: We provide the first linear-time algorithm for 1-center problem in fixed-dimensional ℓ_1 metrics. On the other hand,arXiv:2112.03222v1 fatcat:qlknjrjlqzdtdely3eq45cvsmu