  We study the point location problem on dynamic planar subdivisions that
allows insertions and deletions of edges. In our problem, the underlying graph
of a subdivision is not necessarily connected. We present a data structure of
linear size for such a dynamic planar subdivision that supports sublinear-time
update and polylogarithmic-time query. Precisely, the amortized update time is
$O(\sqrt{n}\log n(\log\log n)^{3/2})$ and the query time is $O(\log n(\log\log
n)^2)$, where $n$ is the number of edges in the subdivision. This answers a
question posed by Snoeyink in the Handbook of Computational Geometry. When only
deletions of edges are allowed, the update time and query time are just
$O(\alpha(n))$ and $O(\log n)$, respectively.
