In mathematics, a '''submodular set function''' (also known as a '''submodular function''') is a [[set function]] whose valuethat, informally, hasdescribes the propertyrelationship thatbetween thea difference in the incremental valueset of theinputs functionand thatan aoutput, singlewhere elementadding makesmore whenof added to anone input sethas decreasesa asdecreasing theadditional sizebenefit of([[diminishing the input set increasesreturns]]). Submodular functions have aThe natural [[diminishing returns]] property which makes them suitable for many applications, including [[approximation algorithms]], [[game theory]] (as functions modeling user preferences) and [[electrical network]]s. Recently, submodular functions have also found immense utility in several real world problems in [[machine learning]] and [[artificial intelligence]], including [[automatic summarization]], [[multi-document summarization]], [[feature selection]], [[Active learning (machine learning)|active learning]], sensor placement, image collection summarization and many other domains.<ref name="LB" /><ref name="TIWB" /><ref name="KG1" /><ref name="KG" />
