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Submodular set function - Wikipedia

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In mathematics, a submodular set function (also known as a submodular 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 (diminishing returns). The natural diminishing returns property which makes them suitable for many applications, including approximation algorithms, game theory (as functions modeling user preferences) 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.[1][2][3][4] If Ω is a finite set, a submodular function is a set function 𝑓 : 2 Ω → 𝑅 , where 2 Ω denotes the power set of Ω , which satisfies one of the following equivalent conditions.[5] A nonnegative sub

Submodular set function - Wikipedia Jump to content From Wikipedia, the free encyclopedia Set-to-real map with diminishing returns In mathematics, a submodular set function (also known as a submodular 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 ( diminishing returns ). The natural diminishing returns property which makes them suitable for many applications, including approximation algorithms , game theory (as functions modeling user preferences) and electrical

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