Approximation Algorithms for the Minimum Convex Partition Problem

  • Christian Knauer
  • Andreas Spillner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4059)


We present two algorithms that compute constant factor approximations of a minimum convex partition of a set P of n points in the plane. The first algorithm is very simple and computes a 3-approximation in O(n logn) time. The second algorithm improves the approximation factor to \(\frac{30}{11} < 2.7273\) but it is more complex and a straight forward implementation will run in O(n 2) time. The claimed approximation factors are proved under the assumption that no three points in P are collinear. As a byproduct we obtain an improved combinatorial bound: there is always a convex partition of P with at most \(\frac{15}{11}n -- \frac{24}{11}\) convex regions.


Approximation Algorithm Convex Hull Convex Polygon Convex Region Collinear Point 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Christian Knauer
    • 1
  • Andreas Spillner
    • 2
  1. 1.Institute of Computer ScienceFreie UniversitätBerlin
  2. 2.Institute of Computer ScienceFriedrich-Schiller-UniversitätJena

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