Before revision: We study a family of clustering problems that require fault-tolerant solutions that are also robust with the presence of outliers.
After revision: In many fundamental combinatorial optimization problems, a feasible solution induces some real cost vectors as an intermediate result, and the optimization objective is a certain function of the vectors. For example, in the problem of makespan minimization on unrelated parallel machines, a feasible job assignment induces a vector containing the sizes of assigned jobs for each machine, and the goal is to minimize the L_\infty norm of L_1 norms of the vectors. Another example is fault-tolerant solutions that are also robust with the presence of outliers.