Suppose we have two directed acyclic graphs $A$ and $B$ and we look to find the subgraph that is common to both graphs and has the most number of vertices. That is to find the biggest graph which is a subgraph of both $A$ and $B$. The vertices are not labeled, but of course, the directions on edges do matter.
Noting that this solves the graph isomorphism, the problem is not known to be solvable in polynomial time. So I was looking for an approximation algorithm. Can you think of any?