  We study dynamic planar point location in the External Memory Model or Disk
Access Model (DAM). Previous work in this model achieves polylog query and
polylog amortized update time. We present a data structure with $O( \log_B^2
N)$ query time and $O(\frac{1}{ B^{1-\epsilon}} \log_B N)$ amortized update
time, where $N$ is the number of segments, $B$ the block size and $\epsilon$ is
a small positive constant, under the assumption that all faces have constant
size. This is a $B^{1-\epsilon}$ factor faster for updates than the fastest
previous structure, and brings the cost of insertion and deletion down to
subconstant amortized time for reasonable choices of $N$ and $B$. Our structure
solves the problem of vertical ray-shooting queries among a dynamic set of
interior-disjoint line segments; this is well-known to solve dynamic planar
point location for a connected subdivision of the plane with faces of constant
size.
