Comment by srean

One way to pose/(think about) the problem is that there are two finite metric spaces linked by an unknown odometry (damn you autocorrect). The problem is to recover that unknown isometry.

This, like graph isometry, can be very computationally intensive in the worst case. However, heuristics to aid matching one vertex on one graph to another vertex on another graph using local, semilocal structural signatures can be very effective on particular cases.

One can of course argue that the spaces are not designed as metric spaces. Even if true, these might be metrizable topological spaces.

More generally, if these are indeed non-metric spaces one can still pose it as finding the unknown isomorphism between two poset spaces.

In my other comment I was using the property of maximal chains -- Identify the longest chains in both posets. The isomorphism must map the longest chain in Poset 1 directly to a longest chain in Poset 2, preserving the exact linear order.