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Computing the Visibility Polygon of an Island in a Polygonal Domain

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Automata, Languages, and Programming (ICALP 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7391))

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Abstract

Given a set \(\mathcal{P}\) of h pairwise-disjoint polygonal obstacles of totally n vertices in the plane, we study the problem of computing the (weakly) visibility polygon from a polygonal obstacle P * (an island) in \(\mathcal{P}\). We give an O(n 2 h 2) time algorithm for it. Previously, the special case where P * is a line segment was solved in O(n 4) time, which is worst-case optimal. In addition, when all obstacles in \(\mathcal{P}\) (including P *) are convex, our algorithm runs in O(n + h 4) time.

This research was supported in part by NSF under Grant CCF-0916606.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA

    Danny Z. Chen & Haitao Wang

Authors
  1. Danny Z. Chen
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  2. Haitao Wang
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Centre for Discrete Mathematics and its Applications, University of Warwick, Warwick, UK

    Artur Czumaj

  2. Max-Planck-Institut für Informatik, Saarbrücken, Germany

    Kurt Mehlhorn

  3. Computer Laboratory, University of Cambridge, UK

    Andrew Pitts

  4. ETH Zurich, Switzerland

    Roger Wattenhofer

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© 2012 Springer-Verlag Berlin Heidelberg

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Chen, D.Z., Wang, H. (2012). Computing the Visibility Polygon of an Island in a Polygonal Domain. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds) Automata, Languages, and Programming. ICALP 2012. Lecture Notes in Computer Science, vol 7391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31594-7_19

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  • DOI: https://doi.org/10.1007/978-3-642-31594-7_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31593-0

  • Online ISBN: 978-3-642-31594-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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