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 {\em 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 standard binary-search-based queries on the convex hull of $S$ can be answered in $O(\log h)$ time, where $h$ is the number of vertices of the convex hull of $S$, and the convex hull itself can be output in $O(h)$ time.

翻译：考虑在平面点集 $S$ 上维护凸包的动态问题，其中插入和删除操作遵循以下特殊序列（称为{\em 窗口滑动更新}）：在 $S$ 所有点的右侧插入一个点，并删除 $S$ 的最左点。本文提出一种占用 $O(|S|)$ 空间的数据结构，每次更新可在均摊 $O(1)$ 时间内完成，且基于二分查找的凸包查询可在 $O(\log h)$ 时间内回答（其中 $h$ 为 $S$ 的凸包顶点数），凸包本身可在 $O(h)$ 时间内输出。