Submodular set function

Set-to-real map with diminishing returns

In mathematics, a submodular set function is a set function that, informally, describes the relationship between a set of inputs and an output, where adding more of one input has a decreasing additional benefit. The natural diminishing returns property which makes them suitable for many applications, including approximation algorithms, game theory and electrical networks. Recently, submodular functions have also found utility in several real world problems in machine learning and artificial intelligence, including automatic summarization, multi-document summarization, feature selection, active learning, sensor placement, image collection summarization and many other domains.

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