Submodular function

A function $f(a,b)$ is submodular iff

$a_{1}<a_{2},b_{1}<b_{2}\Longrightarrow f(a_{1},b_{1})+f(a_{2},b_{2})\leq f(a_{1},b_{2})+f(a_{2},b_{1})$

If the inequality is reversed, the function is supermodular, and if the inequality is changed to an equality, the function is modular.