Tight Time Bounds for the Minimum Local Convex Partition Problem

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


Let v be a vertex with n edges incident to it, such that the n edges partition an infinitesimally small circle C around v into convex pieces. The minimum local convex partition (MLCP) problem asks for two or three out of the n edges that still partition C into convex pieces and that are of minimum total length. We present an optimal algorithm solving the problem in linear time if the edges incident to v are sorted clockwise by angle. For unsorted edges our algorithm runs in O(n log n) time. For unsorted edges we also give a linear time approximation algorithm and a lower time bound.


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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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