Simultaneous Source Location

We consider the problem of Simultaneous Source Location selecting locations for sources in a capacitated graph such that a given set of demands can be satisfied. We give an exact algorithm for trees and show how this can be combined with a result of Racke to give a solution that exceeds edge capacities by at most O(log(2) n log log n), where n is the number of nodes. On graphs of bounded treewidth, we show the problem is still NP-Hard, but we are able to give a PTAS with at most O(1+epsilon) violation of the capacities, or a (k+1)-approximation with exact capacities, where k is the treewidth and epsilon can be made arbitrarily small.