Dynamic Planar Convex Hull

Gerth Stølting Brodal and Riko Jacob

In Proc. 43rd Annual Symposium on Foundations of Computer Science, pages 617-626, 2002.


In this paper 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 n points in the plane under 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.

Copyright notice

Copyright © 2002 by The Institute of Electrical and Electronics Engineers, Inc. All rights reserved.

Online version

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BIBTEX entry

  author = "Gerth St{\o}lting Brodal and Riko Jacob",
  booktitle = "Proc. 43rd Annual Symposium on Foundations of Computer Science",
  doi = "10.1109/SFCS.2002.1181985",
  isbn = "0-7695-1822-2",
  pages = "617-626",
  title = "Dynamic Planar Convex Hull",
  year = "2002"