Maximize a Monotone Function with a Generic Submodularity Ratio

Generic submodularity ratio \(\gamma \) is a general measurement to characterize how close a nonnegative monotone set function is to be submodular. In this paper, we make a systematic analysis of greedy algorithms for maximizing a monotone and normalized set function with a generic submodularity ratio \(\gamma \) under Cardinality constraints, Knapsack constraints, Matroid constraints and K-intersection constraints.

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