Supermodular function: Difference between revisions

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definition of supermodular set functions was the one of submodular set functions
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# <math> f(A)+f(B) \leq f(A \cap B) + f(A \cup B) </math> for all <math> A, B \subseteq S </math>.
# <math> f(A \cup \{v\}) - f(A) \geqleq f(B \cup \{v\}) - f(B) </math> for all <math> A \subset B \subset V </math>, where <math> v \notin B </math>.
 
A set function <math>f</math> is submodular if <math>-f</math> is supermodular, and modular if it is both supermodular and submodular.