Dynamic Convex Hulls under Window-Sliding Updates
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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 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.
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