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Integer programming regards optimization problems, where one seeks to find integer values for a set of unknowns, that optimizes the objective function. A common subset of this type of problems are integer linear programming problems, where all inequalities, equalities and the objective function are linear in the unknowns.

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Maximize sum of supermodular functions over nested sets

Let $R$ be a function that maps a set and a positive integer to a real positive number. We have that for any positive integer $t$ and $S \subseteq \{1, \ldots, t\}$, $R(S, t)$ satisfies: For all $t …