Dynamic Planar Convex hull

Riko Jacob

May 2002


We determine the computational complexity of the dynamic convex hull problem in the planar case. We present a data structure that maintains a finite set of points in the plane under insertion and deletion of points in amortized $O(\log n)$ time. Here n denotes the number of points in the set. The data structure supports the reporting of the extreme point of the set in some direction in worst-case and amortized $O(\log n)$ time. The space usage of the data structure is $O(n)$. We give a lower bound on the amortized asymptotic time complexity that matches the performance of this data structure

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