Dilation-Optimal Edge Deletion in Polygonal Cycles

  • Hee-Kap Ahn
  • Mohammad Farshi
  • Christian Knauer
  • Michiel Smid
  • Yajun Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4835)


Let C be a polygonal cycle on n vertices in the plane. A randomized algorithm is presented which computes in O(n log3 n) expected time, the edge of C whose removal results in a polygonal path of smallest possible dilation. It is also shown that the edge whose removal gives a polygonal path of largest possible dilation can be computed in O(n logn) time. If C is a convex polygon, the running time for the latter problem becomes O(n). Finally, it is shown that for each edge e of C, a (1 − ε)-approximation to the dilation of the path C ∖ {e} can be computed in O(n logn) total time.


Convex Polygon Voronoi Cell Recursive Call Lower Envelope Expected Time 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Hee-Kap Ahn
    • 1
  • Mohammad Farshi
    • 2
    • 4
  • Christian Knauer
    • 3
  • Michiel Smid
    • 4
  • Yajun Wang
    • 5
  1. 1.Department of Computer Science and Engineering, POSTECH, PohangKorea
  2. 2.Department of Mathematics and Computing Science, TU Eindhoven, P.O. Box 513, 5600 MB EindhovenThe Netherlands
  3. 3.Institut für Informatik, Freie Universität Berlin, Takustraße 9, D–14195 BerlinGermany
  4. 4.School of Computer Science, Carleton University, Ottawa, Ontario, K1S 5B6Canada
  5. 5.Department of Computer Science and Engineering, HKUST, Hong Kong S.A.RChina

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