co.combinatorics - Remove unnecessary dependencies in a task graph?

For each vertex x, make a set that contain each vertex y that can reach x. This sets also includes x.

If you have two edges b -> a and c -> a, then if the set associated with b is a subset of the set associated with c, then the edge b -> a can be removed.

Example:

a -> b
b -> c
a -> c

The set are:
a: { a }
b: { a, b } // Can be reached from a and b
c: { a, b, c}

If you look at the edges:
b -> c
a -> c

Then you see that the set of a is a subset of b. So, the edge a -> c can be removed.

Lucas