Numerous combinatorial optimization problems (knapsack, maximum-weight matching, etc.) can be expressed as subset maximization problems: One is given a ground set $$N=\{1,\dots ,n\}$$ , collection $$\mathcal {F}\subseteq 2^N$$ of subsets thereof such that $$\emptyset \in \mathcal {F}$$ and an objective (profit) function $$p:\mathcal {F}\rightarrow \mathbb {R}_+$$ . The task to choose $$S\in max...
