  We solve the equivalence problem for vacuum PP-wave spacetimes by employing
the Karlhede algorithm. Our main result is a suite of Cartan invariants that
allows for the complete invariant classification of the vacuum pp-waves. In
particular, we derive the invariant characterization of the G2 and G3
sub-classes in terms of these invariants. It is known [Collins91] that the
invariant classification of vacuum pp-waves requires at most the fourth order
covariant derivative of the curvature tensor, but no specific examples
requiring the fourth order were known. Using our comprehensive classification,
we prove that the q<=4 bound is sharp and explicitly describe all such maximal
order solutions.
