Is there an efficient method to store large DAGs? I have a DAG representing strict partial order where each node is an assignment of variables $V$ to their values $v$. Each arc $(u,w)$ represents a change in one variable value such that $u\succ w$. 

So if I have $n$ binary variables, I will end up with $2^n$ nodes which is exponential to the size of variables $n$. is there any method to store such DAG efficiently?
Try constructing a reduced ordered binary decision diagram (ROBDD) as described here. 
The reducing algorithm removes redundant nodes, and reuses equal subtrees in the decision tree, such that every node is unique.
The memory complexity of a ROBDD is $\mathcal O({2^n \over n})$ as proved here.