  We consider the problem of allocating a fixed amount of resource among nodes
in a network when each node suffers a cost which is a convex function of the
amount of resource allocated to it. We propose a new deterministic and
distributed protocol for this problem. Our main result is that the associated
convergence time for the global objective scales quadratically in the number of
nodes on any sequence of time-varying undirected graphs satisfying a long-term
connectivity condition.
