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Consider the problem of finding a point in a metric space ({1, 2, . . . , n}, d) with the minimum average distance to other points. We show that this problem has no deterministic o(n 1+1/(h−1) )-query (2h−Ω(1))-approximation algorithms for any constant h ∈ Z + \ {1}.

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We give a deterministic O(hn 1+1/h )-time (2h)-approximation nonadaptive algorithm for 1-median selection in n-point metric spaces, where h ∈ Z + \ {1} is arbitrary. Our proof generalizes that of Chang [2].

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