tree - What algorithm can I apply to this DAG? -

I have a DAG representing the list of properties, these properties are such that if A> B, then a guided Edge b also is transitive, so if A> B and B> C, then there is a guided edge for C.

However, the directional edge of A to C is very important because the directional edge for a directed edge B and B is C. How can I sort all these unnecessary edges? I was thinking of using the minimum Fannie tree algorithm, but I'm not sure what is the appropriate algorithm for applying in this situation

I think I am deep in my node Do the first discovery and compare all its outgoing edges and if it can reach some nodes without using some edges, but it looks very inefficient and slow.

Once the algorithm is complete, the output order will have a linear list of all the nodes which correspond to the graph, so if someone has three guided edges B, C, and D, B and C, each of which D's are guided edges, output can be either ABCD or ADBD.

It is called. Speaking formally, you are looking for at least (the lowest edges) guided graphs, which is equivalent to the transitive closure of the input graph for transitive closing. (This is evident from the diagram given on the Wikipedia link above.)

Apparently there is an efficient algorithm for solving this problem which at the same time takes an infectious shutdown ( I.e. the more common inverse problem of adding the transit link rather than the removal of them), although downloading by AHO, Gary and Ulman costs $ 25, and some Quick Goggles has not given any good description Is.

Edit: Includes! This Java Library is very well-organized.