Dynamic Planar Convex Hull with Optimal Query Time and O(log n · log log n) Update Time

  • Gerth Stølting Brodal
  • Riko Jacob
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1851)


The dynamic maintenance of the convex hull of a set of points in the plane is one of the most important problems in computational geometry. We present a data structure supporting point insertions in amortized O(log n · log log log n) time, point deletions in amortized O(log n · log log n) time, and various queries about the convex hull in optimal O(log n) worst-case time. The data structure requires O(n) space. Applications of the new dynamic convex hull data structure are improved deterministic algorithms for the k-level problem and the red-blue segment intersection problem where all red and all blue segments are connected.


Convex Hull Computational Geometry Query Time Insertion Time Query Structure 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Gerth Stølting Brodal
    • 1
  • Riko Jacob
    • 1
  1. 1.BRICS, Department of Computer ScienceUniversity of AarhusDenmark

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