The inverse p-median problem consists in changing the weights of the customers of a p-median location problem at minimum cost such that a set of p prespeciÿed suppliers becomes the p-median. The cost is proportional to the increase or decrease of the corresponding weight. We show that the discrete version of an inverse p-median problem can be formulated as a linear program. Therefore, it is polynomially solvable for ÿxed p even in the case of mixed positive and negative customer weights. In the

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... case of trees with nonnegative vertex weights, the inverse 1-median problem is solvable in a greedy-like fashion. In the plane, the inverse 1-median problem can be solved in O(n log n) time, provided the distances are measured in l1or l∞-norm, but this is not any more true in R 3 endowed with the Manhattan metric.