# Define a directed edge in a DAG using partial ordering

I am trying to describe a novel type of DAG's construction algorithm (in computer science). The directed edges of the graph correspond to a partial ordering: i.e. any directed edge $$e$$ spanning from $$f$$ to $$t$$ also observes: $$f \preceq t$$.

Q: How can I precisely define the main task of edge construction: that is finding the node $$f$$ for a given $$t$$?

It is something like this:

find all $$f_a \in \{ f_i \}$$ s.t. $$f_a \preceq t$$ $$\land \nexists f_j$$ s.t. $$f_i \preceq f_j$$

but I'm not sure if this is sufficient or even understandable?

• Like a Hasse diagram of the poset? you want the notion of covering? en.wikipedia.org/wiki/Covering_relation Jan 23 at 11:09
• The graph is a DAG where the edges are added according to a partial ordering of the nodes. It is not the goal to try to visualize the partial ordering using a pre-defined diagram. Maybe I should ask on the cs stackexchange instead :/
– Domi
Jan 23 at 11:50
• Well, just give us an example, so we know what you are doing. The statement that you have is a little vague and, perhaps, we can help to formalize it. Jan 23 at 13:39
• Ok, sounds like a en.wikipedia.org/wiki/Dependency_graph to me. Please edit the question when you can give us the "rule set". Jan 23 at 13:49
• @MishaLavrov I agree. I also came to the conclusion that a short, concise "wordy" version might be more useful than an attempt at pseudo symbolism, or so I think... I will see as I draw up a concept graph etc. A few picture and examples can probably also aid the definition... Or so I hope
– Domi
Jan 23 at 18:46