Before revision:  In order to address the fairness concern, we also consider variants of the aforementioned problems, namely fair robust fault-tolerant center problems. In these problems, each client j has a value e_j, and we need to stochastically open a set of facilities such that the expected number of facilities that are assigned to j is at least e_j. We develop a pure approximation for fair robust fault-tolerant k-center and multi-criteria approximation algorithms for the knapsack and matroid variations .
After revision:  In order to address the fairness concern, we also consider variants of the aforementioned problems, namely fair robust fault-tolerant k-center and multi-criteria approximation algorithms for the knapsack and matroid variations .