Anyone seen the "Minimize the Maximum Load on a Node" problem in the context of facility location?

Hi all,
I have trying to search all over for work on this, but have not been successful. I hope someone on this group can shed some light on this:

The problem is essentially a modification of the facility location problem:

[begin problem]
Given: Graph G<V,E> and a natural number 'k'
To do: Divide V into two sets B [big] with cardinality k and S[small] (= V-B) nodes and find a path from each node in S to some node in B so that the following is satisfied:

[up to here, it is exactly like the classic facility location problem]

If p_u = The number of paths passing through node u [u in S]

Find the set B and the paths such that
max {p_u, u in S}
is minimized.
[end problem]

The context is that each "small" node in the network wants to send a packet to one of the "Big" nodes, the other small nodes routing the message; and what we want to minimize is not the sum of the path-lengths but the routing-load of the most-loaded small node.

I will be extremely grateful if someone could
1. Point me to an existing algorithm for optimally solving this, even for G being a tree. or
2. Point me to an existing proof of NP-hardness. or
3. Point me to some existing NP-hard problems which can used for reduction to this problem.

Thanks a lot.
Animesh Pathak
Grad. Student,
Computer Engg.
USC
animesh@xxxxxxx
.