  We provide an efficient reduction from the problem of querying approximate
multiplicatively weighted farthest neighbors in a metric space to the
unweighted problem. Combining our techniques with core-sets for approximate
unweighted farthest neighbors, we show how to find (1+epsilon)-approximate
farthest neighbors in time O(log n) per query in D-dimensional Euclidean space
for any constants D and epsilon. As an application, we find an O(n log n)
expected time algorithm for choosing the center of a star topology network
connecting a given set of points, so as to approximately minimize the maximum
dilation between any pair of points.
