  In the classical facility location problem we consider a graph $G$ with fixed
weights on the edges of $G$. The goal is then to find an optimal positioning
for a set of facilities on the graph with respect to some objective function.
We introduce a new framework for facility location problems, where the weights
on the graph edges are not fixed, but rather should be assigned. The goal is to
find a valid assignment for which the resulting weighted graph optimizes the
facility location objective function. We present algorithms for finding the
optimal {\em budget allocation} for the center point problem and for the median
point problem on trees. Our algorithms run in linear time, both for the case
where a candidate vertex is given as part of the input, and for the case where
finding a vertex that optimizes the solution is part of the problem. We also
present a hardness result for the general graph case of the center point
problem, followed by an $O(\log^2(n))$ approximation algorithm on graphs - with
general metric spaces.
