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The paper is divided into two main sections. The first deals with a multidimensional search technique of Megiddo [J. Assoc. Comput. Mach., 31 (1984), pp. 114–127], and suggests an improvement. The second gives an application of the technique to the Euclidean one-centre problem in Rᵈ. An algorithm of time-complexity O(3(d + 2)² n) is derived for this problem. This improves the best previous bound even in the case $d = 2$.
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Martin Dyer (1986) studied this question.
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