Approximability of the dispersed (p)over-right-arrow-neighbor k-supplier problem

We consider the dispersed (p) over right arrow -neighbor k-supplier problem. In the classical k-supplier problem, we have to select k suppliers in a metric space such that the maximum distance between a customer and its closest supplier is minimized. Here, we generalize this problem to the case where each customer possibly needs service from more than one supplier. Moreover, the selected suppliers should not be too close to each other, i.e., they need to be dispersed. For the classical k-supplier problem, and its special case the k-center problem, there is a 3- and a 2-approximation respectively. We show that these guarantees can also be given in the case when customers need service from multiple suppliers, without imposing dispersion constraints. If we generalize the problem to the dispersed case, without imposing neighboring constraints, we get inapproximability results depending on the measure of dispersion. We also show (almost) matching upper bounds. Finally, we show that adding both the neighbor requirement and the dispersion requirement leads to an inapproximable problem. (c) 2020 Elsevier B.V. All rights reserved.