  We consider the directed Hausdorff distance between point sets in the plane,
where one or both point sets consist of imprecise points. An imprecise point is
modelled by a disc given by its centre and a radius. The actual position of an
imprecise point may be anywhere within its disc. Due to the direction of the
Hausdorff Distance and whether its tight upper or lower bound is computed there
are several cases to consider. For every case we either show that the
computation is NP-hard or we present an algorithm with a polynomial running
time. Further we give several approximation algorithms for the hard cases and
show that one of them cannot be approximated better than with factor 3, unless
P=NP.
