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

It seems to be more of an answer than a comment so I'll post it

The documentation says:

It follows immediately from the contract for compare that the quotient is an equivalence relation on S, and that the imposed ordering is a total order on S."

So no, a Comparator requires a total ordering. If you implement this with a partial ordering you're breaching the interface contract.

Even if it might work in some scenario, you should not attempt to solve your problem in a way that breaches the contract of the interface.

See this question about data structures that do fit a partial ordering.