algorithmic problem

[gusl]

Given a set L of permutations of a list, compute the maximal partial order (DAG) under which all lists in L are topological sorts. How would you do this? Can you do better than O(m n^2 k^2)? (m = number of lists in L, k = # of things in domain = the size of the elements of L)
Sounds like an ILP problem.

One idea: whenever a cycle is detected, all the elements are deemed incomparable.