Need help understanding this optimization problem on graphs
You can think of the parent sets as incident nodes; that is if $V_i$ is in the parent set of $V_j$, there is a (directed) edge from $V_i$ to $V_j$.

An ordering "consistent" with this graph in the sense of the exercise is a topological sorting, that is a topological ordering $V_{\pi(1)}, \dots, V_{\pi(n)}$ has no pair $(i,j)$ with $i&lt;j$ so that there is an edge from $V_{\pi(j)}$ to $V_{\pi(i)}$.

The problem is then to find an ordering as consistent with the graph as possible.