Submodular optimization plays a key role in many real-world problems. In many real-world scenarios, it is also necessary to handle uncertainty, and potentially disruptive events that violate constraints in stochastic settings need to be avoided. In this paper, we investigate submodular optimization problems with chance constraints. We provide a first analysis on the approximation behavior of popular greedy algorithms for submodular problems with chance constraints. Our results show that these algorithms are highly effective when using surrogate functions that estimate constraint violations based on Chernoff bounds. Furthermore, we investigate the behavior of the algorithms on popular social network problems and show that high quality solutions can still be obtained even if there are strong restrictions imposed by the chance constraint. Submodular optimization has been studied for a wide range of different constraint types, see, for example, (KG14) and references mentioned therein. Many of the results on monotone submodular functions are based on simple greedy selection strategies that are able to achieve provably the best
Doerr et al. REF have investigated adaptations of classical greedy algorithms for the optimization of submodular functions with chance constraints of knapsack type.
Optimization of Chance-Constrained Submodular Functions
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Computer Science Mathematics