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We present new tight performance guarantees for the greedy maximization ofnondecreasing submodular set functions. Our main result first provides aperformance guarantee in terms of the overlap of the optimal and greedysolutions. As a consequence we improve performance guarantees of Nemhauser,Wolsey and Fisher (1978) and Conforti and Cornu\'ejols (1984) for maximizationover subsets, which are at least half the size of the problem domain. As afurther application, we obtain a new tight performance guarantee in terms ofthe cardinality of the problem domain.

New performance guarantees for the greedy maximization of submodular set functions