Algorithms for the Minimum Diameter of Moving Points and for the Discrete 1-center problem

Given points moving with constant, but possibly different, velocities,the moving diameter problem is to find the minimum, over all time, ofthe maximum distance between a pair of points at each moment. Thisnote gives a randomized algorithm requiring O(n log n) expected timefor this problem, in two and three dimensions. Also briefly noted is arandomized O(n log n log log n) expected-time algorithm for the discrete1-center problem in three dimensions; in this problem, a member p of aset S...