On a Multidimensional Search Technique and its Application to the Euclidean One-Centre Problem

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 $\mathbb{R}^d $. 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 $d = 2$.