We propose a dynamic data structure for the distribution-sensitive point location problem in the plane. Suppose that there is a fixed query distribution within a convex subdivision
S
, and we are given an oracle that can return in
O
(1) time the probability of a query point falling into a polygonal region of constant complexity. We can maintain
S
such that each query is answered in
O
opt
(S)
) expected time, where opt (
S
) is the expected time of the best linear decision tree for answering point location queries in
S
. The space and construction time are
O(n
log
2
n
), where
n
is the number of vertices of
S
. An update of
S
as a mixed sequence of
k
edge insertions and deletions takes
O(k
log
4
n) amortized time. As a corollary, the randomized incremental construction of the Voronoi diagram of
n
sites can be performed in
O(n
log
4
n
) expected time so that, during the incremental construction, a nearest neighbor query at any time can be answered optimally with respect to the intermediate Voronoi diagram at that time.
Dynamic Distribution-Sensitive Point Location
