Submodular set function: Difference between revisions

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Revision as of 22:26, 1 October 2011

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A '''submodularSubmodular function''' is a set function <math>f:2^{\Omega}\rightarrow R</math> such that for any <math>X\subseteq Y\subseteq \Omega</math>

'''Submodular functions''' ...

A '''submodular function''' is a set function <math>f:2^{\Omega}\rightarrow R</math> such that for any <math>X\subseteq Y\subseteq \Omega</math>

and <math>x\in \Omega\backslash X</math> we have that <math>f(X\cup \{x\})-f(X)\geq f(Y\cup \{x\})-f(Y)</math>

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# Graph cuts

# Coverage function

# [[Entropy (information theory)|Entropy]]

# [[Mutual information]]

# Mututal Information

# [[Matroid]] rank functions

==Optimization Problems==

# Minimization

# Maximization

== References ==

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== External links ==

* [http://www.example.com/ example.com]

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