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Best Algorithms for Approximating the Maximum of a Submodular Set Function
Mathematics of Operations Research, 1978A real-valued function z whose domain is all of the subsets of N = {1, …, n) is said to be submodular if z(S) + z(T) ≥ z(S ∪ T) + z(S ∩ T), ∀S, T ⊆ N, and nondecreasing if z(S) ≤ z(T), ∀S ⊂ T ⊆ N. We consider the problem max S⊂N {z(S): |S| ≤ K, z submodular and nondecreasing, z(Ø) = 0}.
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