Given a complete graph $G(V,E)$, for each $v \in V$, there is a weight $f(v) \in \Bbb N$, similarly for each $e \in E$, there is a weight $g(e) \in \Bbb N$. The problem is for a fixed $L$ select a complete subgraph $S(V',E')$ which has minimum $|V'|$ and $\sum_{v \in V'} f(v)-\sum_{e \in E'} g(e) \ge L$. Is there some advice or relative solved problem? Thanks guys.
find the subgraph with minimum vertexes that satisfied one constrain
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graph-theory
optimization