There has been a fair amount of work on computational problems for partial orders (e.g., recognition, jump number, comparability graph recognition, etc...).
I am curious what work specific to lattices has been done. I have searched around and not found much similar work for lattices.
In particular, I am interested in whether the following lattice problems have been investigated:
Lattice recognition: given a DAG or a partial order is it in fact a lattice?
Lattice comparability graph recognition: given a undirected graph G, can the edges of G be oriented such that the resulting orientation is a lattice?
Determining/counting the join irreducible elements of a lattice
Determining if a given lattice is distributed/modular