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Submodular set function
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<p> In mathematics, a submodular set function (also known as a submodular function) is a <a href="/facts/Set_function/Dy46B9EJ">set function</a> that, informally, describes the relationship between a set of inputs and an output, where adding more of one input has a decreasing additional benefit (<a href="/facts/Diminishing_returns/YNwQIqtK">diminishing returns</a>). The natural <a href="/facts/Diminishing_returns/YNwQIqtK">diminishing returns</a> property which makes them suitable for many applications, including <a href="/facts/Approximation_algorithms/BWlf7M32">approximation algorithms</a>, <a href="/facts/Game_theory/zkEIj1ya">game theory</a> (as functions modeling user preferences) and <a href="/facts/Electrical_network/zt94kTW0">electrical networks</a>. Recently, submodular functions have also found utility in several real world problems in <a href="/facts/Machine_learning/e0w0XJTu">machine learning</a> and <a href="/facts/Artificial_intelligence/lJGauQwX">artificial intelligence</a>, including <a href="/facts/Automatic_summarization/yTQYaEIe">automatic summarization</a>, <a href="/facts/Multi-document_summarization/PCyGmnLm">multi-document summarization</a>, <a href="/facts/Feature_selection/gxbuF4VG">feature selection</a>, <a href="/facts/Active_learning_(machine_learning)/wWoXGdCV">active learning</a>, sensor placement, image collection summarization and many other domains. </p>