Partial ordered Comparator

Question

How to implement java.util.Comparator that orders its elements according to a partial order relation?

For example given a partial order relation a

Answer 1

If a < b and b < c implies a < c, then you have made a total ordering by using the hashCodes. Take a < d, d < c. The partial order says that b and d not necessarily are ordered. By introducing hashCodes you provide an ordering.

Example: is-a-descendant-of(human, human).

Adam (hash 42) < Moses (hash 17), Adam < Joe (hash 9)

Implies

Adam < Joe < Moses

A negative example would be the same relation, but when time travel allows being your own descendant.