Time and Space Tradeoffs in Point Location

We preprocess the input subdivision with
$n$
points on the plane in
$O(n\sqrt{\log n})$
time and store them in
$O(n/t)$
space to facilitate point location in
$O(\log t)$
time, where
$t$
is an adjustable parameter. When
$t$
is a constant we get
$O(n)$
space and constant time. When
$t=O(n)$
we get constant space and
$O(\log n)$
time.