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A Faster Algorithm for Computing Straight Skeletons

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Algorithms - ESA 2014 (ESA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8737))

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Abstract

We present a new algorithm for computing the straight skeleton of a polygon. For a polygon with n vertices, among which r are reflex vertices, we give a deterministic algorithm that reduces the straight skeleton computation to a motorcycle graph computation in O(n (logn)logr) time. It improves on the previously best known algorithm for this reduction, which is randomized, and runs in expected \(O(n \sqrt{h+1}\log^2 n)\) time for a polygon with h holes. Using known motorcycle graph algorithms, our result yields improved time bounds for computing straight skeletons. In particular, we can compute the straight skeleton of a non-degenerate polygon in O(n (logn) logr + r 4/3 + ε) time for any ε > 0. On degenerate input, our time bound increases to O(n (logn) logr + r 17/11 + ε).

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Cheng, SW., Mencel, L., Vigneron, A. (2014). A Faster Algorithm for Computing Straight Skeletons. In: Schulz, A.S., Wagner, D. (eds) Algorithms - ESA 2014. ESA 2014. Lecture Notes in Computer Science, vol 8737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44777-2_23

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  • DOI: https://doi.org/10.1007/978-3-662-44777-2_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44776-5

  • Online ISBN: 978-3-662-44777-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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