  In this paper, we study the problem of opening centers to cluster a set of
clients in a metric space so as to minimize the sum of the costs of the centers
and of the cluster radii, in a dynamic environment where clients arrive and
depart, and the solution must be updated efficiently while remaining
competitive with respect to the current optimal solution. We call this dynamic
sum-of-radii clustering problem.
  We present a data structure that maintains a solution whose cost is within a
constant factor of the cost of an optimal solution in metric spaces with
bounded doubling dimension and whose worst-case update time is logarithmic in
the parameters of the problem.
