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In mathematics, submodular functions are set functions which usually appear in approximation algorithms, functions modeling user preferences in game theory,economics, combinatorial optimization, electrical networks and operations research.

Submodularity directly implies the following inequality, for $k \in \{1,\ldots,n-1\}$: $$F(k) \geq \frac{1}{2} F(k+1) + \frac{1}{2} F(k-1).$$ Imagine applying this inequality over and over again, in …
\end{multline*}$$Taking C = A\cup B, this property implies monotone submodularity. Is this property known? Background This property came up while trying to characterize coverage functions. … asked Apr 2 '12 by Yuval Filmus Higher-order discrete derivatives of set functions are explored in Submodularity, supermodularity and higher-order monotonicities of pseudo-boolean functions. … \end{multline*}$$ If you put $C = \varnothing$, you get submodularity. …
The problem of unconstrained submodular maximization can be phrased as follows: Given a non-negative submodular function $f$ on a domain $D$ find a set $S \subseteq D$ maximizing $f(S)$. Here a …