On the approximation of the Minimum Disturbance p-Facility Location Problem Original Research Article

An n×m non-negative integer matrix D={dij} is given, representing the disturbance that customer i receives by a facility at location j. We consider the problem of finding p facilities so that the maximum, over the n customers, of the sums of their disturbances is minimized. We show that this problem can be deterministically approximated within O(ρ(log n+log p)), where ρ is the ratio between the biggest and the smallest positive entry of D. We obtain this result by first taking a randomized rounding approach to the problem and then by derandomizing the algorithm by the method of conditional probabilities.