# An analysis of approximations for maximizing submodular set functions—I

@article{Nemhauser1978AnAO, title={An analysis of approximations for maximizing submodular set functions—I}, author={George L. Nemhauser and Laurence A. Wolsey and Marshall L. Fisher}, journal={Mathematical Programming}, year={1978}, volume={14}, pages={265-294} }

LetN be a finite set andz be a real-valued function defined on the set of subsets ofN that satisfies z(S)+z(T)≥z(S⋃T)+z(S⋂T) for allS, T inN. Such a function is called submodular. We consider the problem maxS⊂N{a(S):|S|≤K,z(S) submodular}.Several hard combinatorial optimization problems can be posed in this framework. For example, the problem of finding a maximum weight independent set in a matroid, when the elements of the matroid are colored and the elements of the independent set can have no…

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