Abstract
We establish a tight bound on the worst-case combinatorial complexity of the farthest-color Voronoi diagram of line segments in the plane. More precisely, given k sets of total n line segments, the combinatorial complexity of the farthest-color Voronoi diagram is shown to be Θ(kn + h) in the worst case, under any L p metric with 1 ≤ p ≤ ∞, where h is the number of crossings between the n line segments. We also show that the diagram can be computed in optimal O((kn + h)logn) time under the L 1 or L ∞ metric, or in O((kn + h) (α(k) logk + logn)) time under the L p metric for any 1 < p < ∞, where α(·) denotes the inverse Ackermann function.
This research was supported by National Research Foundation of Korea(KRF) grant funded by the Korea government(MEST) (No.2011-0005512).
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Bae, S.W. (2012). Tight Bound for Farthest-Color Voronoi Diagrams of Line Segments. In: Rahman, M.S., Nakano, Si. (eds) WALCOM: Algorithms and Computation. WALCOM 2012. Lecture Notes in Computer Science, vol 7157. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28076-4_7
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DOI: https://doi.org/10.1007/978-3-642-28076-4_7
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