Please excuse or improve the poor title of this question.
My question is rather undirected, but I guess I am trying to find out if I might be missing a keyword for my problem.
So there is plenty of work on sorting algorithms.
Sorting is usually understood as creating a / the one correct total order given a set of elements
X and their pairwise relationship
x >= x' for all
X. Or actually
>= is the total order and the task is to create a sequence or directed graph s.t.
x comes after
Now you want to do the exact same thing, only
>= does not define a total order over
X, but only a partial order.
This seems like a very straightforward generalization that I can only imagine is required quite often. Still, under the term partial order production, I find only very little literature on the topic / task.
Am I missing something?
EDIT: Alternative Formulation
Given a set of elements
X and a function
f that returns the relationship between any two elements
X. Create a DAG with an edge
x->x' if the relationship is
x'->x if the relationship
<. Then create the transitive reduction of the DAG.
<. This is normal sorting.
?(not comparable). This is partial order production.
I would say both are clearly ordering problems, given the relationship function
f (the order) and the elements
X to order.
Still you find so much on case (1) and hardly anything on case (2).