Is there an algorithm to “simplify” the dependency graph?

Question

My problem is very simple, but I don’t know its name and therefore it is difficult to find a solution on my own: How to simplify the dependency graph, for example (where -> means, depends):

A → B → C and A → C

to

 A -> B -> C 

Answer 1

You are looking for a transitional reduction .

For a discussion of algorithms, see Transitive Closure and Reduction .