Dilation-optimal edge deletion in polygonal cycles

Authors:
Hee-Kap Ahn;Mohammad Farshi;Christian Knauer;Michiel Smid;Yajun Wang
Affiliations:
Department of Computer Science and Engineering, POSTECH, Pohang, Korea;Department of Mathematics and Computing Science, TU Eindhoven, Eindhoven, The Netherlands and School of Computer Science, Carleton University, Ottawa, Ontario, Canada;Institut für Informatik, Freie Universität Berlin, Berlin, Germany;School of Computer Science, Carleton University, Ottawa, Ontario, Canada;Department of Computer Science and Engineering, HKUST, Hong Kong S.A.R, China
Venue:
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Year:
2007

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Abstract

Let C be a polygonal cycle on n vertices in the plane. A randomizedalgorithm is presented which computes in O(n log3 n) expectedtime, the edge of C whose removal results in a polygonal path of smallestpossible dilation. It is also shown that the edge whose removal gives apolygonal path of largest possible dilation can be computed in O(n log n)time. If C is a convex polygon, the running time for the latter problembecomes O(n). Finally, it is shown that for each edge e of C, a (1 - Ɛ)-approximation to the dilation of the path C \ {e} can be computed inO(n log n) total time.