Abstract
This paper presents an almost optimal algorithm that computes the Voronoi diagram of a set S of n line segments that may intersect or cross each other. If there are k intersections among the input segments in S, our algorithm takes O(n α(n) logn + k) time, where α(·) denotes the functional inverse of the Ackermann function. The best known running time prior to this work was O((n + k) logn). Since the lower bound of the problem is shown to be Ω(n logn + k) in the worst case, our algorithm is worst-case optimal for k = Ω(n α(n) logn), and is only a factor of α(n) away from the lower bound. For the purpose, we also present an improved algorithm that computes the medial axis or the Voronoi diagram of a polygon with holes.
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2013R1A1A1A05006927).
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Bae, S.W. (2015). An Almost Optimal Algorithm for Voronoi Diagrams of Non-disjoint Line Segments. In: Rahman, M.S., Tomita, E. (eds) WALCOM: Algorithms and Computation. WALCOM 2015. Lecture Notes in Computer Science, vol 8973. Springer, Cham. https://doi.org/10.1007/978-3-319-15612-5_12
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DOI: https://doi.org/10.1007/978-3-319-15612-5_12
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