Dynamic Planar Convex Hull

Riko Jacob, Gerth Brodal

Research output: Working paperResearch


In this article, we determine the amortized computational complexity of the planar dynamic convex hull problem by querying.
We present a data structure that maintains a set of n points in the plane under the insertion and deletion of points in amortized O(log n) time per operation. The space usage of the data structure is O(n). The data structure supports extreme point queries in a given direction, tangent queries through a given point, and queries for the neighboring points on the convex hull in O(log n) time. The extreme point queries can be used to decide whether or not a given line intersects the convex hull, and the tangent queries to determine whether a given point is inside the convex hull.
We give a lower bound on the amortized asymptotic time complexity that matches the performance of this data structure.
Original languageEnglish
Number of pages87
Publication statusPublished - 28 Feb 2019


  • Planar dynamic convex hull
  • Amortized computational complexity
  • Data structures
  • Extreme point queries
  • Asymptotic time complexity


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