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We consider the problem of dynamically maintaining the convex hull of a set
$S$ of points in the plane under the following special sequence of insertions
and deletions (called window-sliding updates): insert a point to the right of
all points of $S$ and delete the leftmost point of $S$. We propose an
$O(|S|)$-space data structure that can handle each update in $O(1)$ amortized
time, such that all standard binary-search-based queries on the convex hull of
$S$ can be answered in $O(\log |S|)$ time, and the convex hull itself can be
output in time linear in the number of its vertices.
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