Fault-Tolerant Center-Type Problems with Robustness and Fairness

In this paper, we study a family of clustering problems that require error-resilient solutions which are also robust against the presence of outlier connections. We consider several variants of the robust fault-tolerant $k$-center, matroid center and knapsack center problems, and develop pure or multi-criteria approximation algorithms for them. Unfairness is common for some clients and they may always be regarded as outliers, so we also consider the fairness problem, and give randomized algorithms that embody lottery models, so that for each client $j$ with its submitted parameter $e_j\geq0$, the expected number of connections for it is at least $e_j$. Our techniques include the design of various linear programs for rounding LP solutions, as well as a primal-dual schema using the ellipsoid algorithm.