Best location of service centers in a treelike network under budget constraints

We consider the problem of locating service centers in a treelike network in order to maximize the serviced population under budget constraints. We show that the problem is NP-hard. In the case where the costs of establishing the service centers are equal for all n cities we obtain the maximum weight k-domination problem. An O(nk²) dynamic programming procedure is given. Then an O(nB²) pseudo-polynomial dynamic programming procedure is presented for the original problem, where B is the budget constraint. Finally a variation of the new left-right dynamic programming technique is applied to obtain a more efficient pseudo-polynomial procedure.