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# Minimizing the difference between two submodular functions<ref name="NB" /> is not only NP hard, but also inapproximable.<ref name="IBUAI" />
# Minimization/maximization of a submodular function subject to a submodular level set constraint (also known as submodular optimization subject to submodular cover or submodular knapsack constraint) admits bounded approximation guarantees.<ref name="IB" />
# Partitioning data based on a submodular function to maximize the average welfare is known as the submodular welfare problem, which also admits bounded approximation guarantees (see [[welfare maximization]]).
== Applications ==
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