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In this paper, we study a novel problem, Minimum Robust Multi-SubmodularCover for Fairness (MinRF), as follows: given a ground set $V$; $m$ monotonesubmodular functions $f_1,...,f_m$; $m$ thresholds $T_1,...,T_m$ and anon-negative integer $r$, MinRF asks for the smallest set $S$ such that for all$i \in [m]$, $\min_{|X| \leq r} f_i(S \setminus X) \geq T_i$. We prove thatMinRF is inapproximable within $(1-\epsilon)\ln m$; and no algorithm, takingfewer than exponential number of queries in term of $r$, is able to output afeasible set to MinRF with high certainty. Three bicriteria approximationalgorithms with performance guarantees are proposed: one for $r=0$, one for$r=1$, and one for general $r$. We further investigate our algorithms'performance in two applications of MinRF, Information Propagation for MultipleGroups and Movie Recommendation for Multiple Users. Our algorithms have shownto outperform baseline heuristics in both solution quality and the number ofqueries in most cases.

Minimum Robust Multi-Submodular Cover for Fairness