A Fixed Parameter Algorithm for the Minimum Number Convex Partition Problem

  • Magdalene Grantson
  • Christos Levcopoulos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3742)


Given an input consisting of an n-vertex convex polygon with k hole vertices or an n-vertex planar straight line graph (PSLG) with k holes and/or reflex vertices inside the convex hull, the parameterized minimum number convex partition (MNCP) problem asks for a partition into a minimum number of convex pieces. We give a fixed-parameter tractable algorithm for this problem that runs in the following time complexities:

– linear time if k is constant,

– time polynomial in n if \(k=O(\frac{{\rm log}n}{{\rm log log}n})\),

or, to be exact, in O(n Open image in new window k \(^{\rm 6{\it k}-5}\) Open image in new window 216k ) time.


Convex Polygon Dynamic Programming Algorithm Clockwise Order Solution Table Current Labelling 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Magdalene Grantson
    • 1
  • Christos Levcopoulos
    • 1
  1. 1.Department of Computer ScienceLund UniversityLundSweden

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