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Workshop on Algorithms and Data Structures

WADS 1991: Algorithms and Data Structures pp 425–436Cite as

Dynamically maintaining the visibility graph

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 519))

Abstract

An algorithm is presented to maintain the visibility graph of a set of N line segments in the plane in O(log2 N+K log N) time, where K is the total number of arcs of the visibility graph that are destroyed or created upon insertion or deletion of a line segment. The line segments should be disjoint, except possibly at their end-points. The algorithm maintains the visibility diagram, a 2-dimensional cell complex whose 0-dimensional cells correspond to arcs of the visibility graph.

The method can also be applied to determine the visibility polygon of a query point, and also to plan the motion of a rod amidst a dynamically changing set of obstacles. The time complexity of both applications meets the optimal time bounds for their static counterparts.

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References

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Author information

Authors and Affiliations

  1. Dept. of Math. and Comp. Sc, University of Groningen, P.O.Box 800, 9700 AV, Groningen, The Netherlands

    Gert Vegter

Authors
  1. Gert Vegter
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Editor information

Frank Dehne Jörg-Rüdiger Sack Nicola Santoro

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© 1991 Springer-Verlag Berlin Heidelberg

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Vegter, G. (1991). Dynamically maintaining the visibility graph. In: Dehne, F., Sack, JR., Santoro, N. (eds) Algorithms and Data Structures. WADS 1991. Lecture Notes in Computer Science, vol 519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028281

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  • DOI: https://doi.org/10.1007/BFb0028281

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54343-5

  • Online ISBN: 978-3-540-47566-8

  • eBook Packages: Springer Book Archive

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