I'm trying to solve a graph problem (it's not for homework, just to practice my skills). A DAG $G(V,E)$ is given, where $V$ is the set of vertices and $E$ the edges. The graph is represented as an adjacency list, so $A_v$ is a set containing all the connections of $v$. My task is to find which vertices are reachable from each vertex $v\in V$. The solution I use has a complexity of  $O(V^3)$, with transitive closure, but i read that in a blog it can be faster, although it didn't reveal how. Could anyone tell me another way (with better complexity) to solve the transitive closure problem in a DAG? 
Efficient algorithm for retrieving the transitive closure of a directed acyclic graph
algorithms;graph theory;graphs