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 log n) 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 log n) total time. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Ahn, H. K., Farshi, M., Knauer, C., Smid, M., & Wang, Y. (2007). Dilation-optimal edge deletion in polygonal cycles. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4835 LNCS, pp. 88–99). Springer Verlag. https://doi.org/10.1007/978-3-540-77120-3_10
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