Document Open Access Logo

Partially Walking a Polygon

Authors Franz Aurenhammer, Michael Steinkogler, Rolf Klein

PDF

File

Thumbnail PDF
PDF
LIPIcs.ISAAC.2018.60.pdf
  • Filesize: 333 kB
  • 9 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Polygon
  • guard walk
  • visibility

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

Deciding two-guard walkability of an n-sided polygon is a well-understood problem. We study the following more general question: How far can two guards reach from a given source vertex while staying mutually visible, in the (more realistic) case that the polygon is not entirely walkable? There can be Theta(n) such maximal walks, and we show how to find all of them in O(n log n) time.

Cite As Get BibTex

Franz Aurenhammer, Michael Steinkogler, and Rolf Klein. Partially Walking a Polygon. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 60:1-60:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.ISAAC.2018.60

Author Details

Franz Aurenhammer
  • Institute for Theoretical Computer Science, University of Technology, Graz, Austria
Michael Steinkogler
  • Institute for Theoretical Computer Science, University of Technology, Graz, Austria
Rolf Klein
  • Universität Bonn, Institut für Informatik, Bonn, Germany

Funding

This work was supported by Project I 1836-N15, Austria Science Fund (FWF).

References

  1. Wolfgang Aigner, Franz Aurenhammer, and Bert Jüttler. On triangulation axes of polygons. Information Processing Letters, 115(1):45-51, 2015. Google Scholar
  2. Franz Aurenhammer, Michael Steinkogler, and Rolf Klein. Maximal two-guard walks in a polygon. In 34nd European Workshop on Computational Geometry, EuroCG 2018, pages 17-22, 2018. Google Scholar
  3. Binay Bhattacharya, Asish Mukhopadhyay, and Giri Narasimhan. Optimal algorithms for two-guard walkability of simple polygons. In Workshop on Algorithms and Data Structures, WADS 2001. Lecture Notes in Computer Science, volume 2125, pages 438-449. Springer, 2001. Google Scholar
  4. Bernard Chazelle, Herbert Edelsbrunner, Michelangelo Grigni, Leonidas Guibas, John Hershberger, Micha Sharir, and Jack Snoeyink. Ray shooting in polygons using geodesic triangulations. Algorithmica, 12(1):54-68, 1994. Google Scholar
  5. Leonidas J Guibas and John Hershberger. Optimal shortest path queries in a simple polygon. Journal of Computer and System Sciences, 39(2):126-152, 1989. Google Scholar
  6. Christian Icking and Rolf Klein. The two guards problem. International Journal of Computational Geometry &Applications, 2(03):257-285, 1992. Google Scholar
  7. L.H. Tseng, Paul Heffernan, and Der-Tsai Lee. Two-guard walkability of simple polygons. International Journal of Computational Geometry &Applications, 8(01):85-116, 1998. Google Scholar
  8. Jorge Urrutia. Art gallery and illumination problems. In Handbook of Computational Geometry, pages 973-1027. Elsevier, 2000. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact