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Maintaining the Visibility Graph of a Dynamic Simple Polygon

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Algorithms and Discrete Applied Mathematics (CALDAM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11394))

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Abstract

We devise a fully-dynamic algorithm for maintaining the visibility graph of a given simple polygon P amid vertex insertions and deletions to the simple polygon. Our algorithm takes \(O(k(\lg {n'})^2)\) worst-case time to update the visibility graph when a vertex is inserted to the current simple polygon \(P'\), or when a vertex is deleted from \(P'\). Here, k is the number of combinatorial changes needed to the visibility graph due to the insertion (resp. deletion) of a vertex v to \(P'\), and \(n'\) is the number of vertices of \(P'\). This algorithm preprocesses the initial simple polygon P to build few data structures, including the visibility graph of P. Further, as part of efficiently updating the visibility graph, a fully-dynamic algorithm is designed to compute the vertices of the current simple polygon that are visible from a query point.

R. Inkulu—This research is supported in part by NBHM grant 248(17)2014-R&D-II/1049.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, IIT Guwahati, Guwahati, India

    Tameem Choudhury & R. Inkulu

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  1. Tameem Choudhury
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  2. R. Inkulu
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Correspondence to R. Inkulu .

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Editors and Affiliations

  1. Indian Institute of Technology, Kharagpur, India

    Sudebkumar Prasant Pal

  2. Cochin University of Science and Technology, Cochin, India

    Ambat Vijayakumar

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Choudhury, T., Inkulu, R. (2019). Maintaining the Visibility Graph of a Dynamic Simple Polygon. In: Pal, S., Vijayakumar, A. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2019. Lecture Notes in Computer Science(), vol 11394. Springer, Cham. https://doi.org/10.1007/978-3-030-11509-8_4

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  • DOI: https://doi.org/10.1007/978-3-030-11509-8_4

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