Binary relations are an important abstraction arising in many data
representation problems. The data structures proposed so far to represent them
support just a few basic operations required to fit one particular application.
We identify many of those operations arising in applications and generalize
them into a wide set of desirable queries for a binary relation representation.
We also identify reductions among those operations. We then introduce several
novel binary relation representations, some simple and some quite
sophisticated, that not only are space-efficient but also efficiently support a
large subset of the desired queries.