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Combinatorics and complexity of guarding polygons with edge and point 2-transmitters
College of Computing, Georgia Institute of Technology, Atlanta, USA.
Paulson School of Engineering and Applied Sciences, Harvard University, MA, USA.
Mathematics Department, The Spence School, NY, USA.
Mathematics Department, Technische Universität Chemnitz, Germany.
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2018 (English)In: Computational geometry, ISSN 0925-7721, E-ISSN 1879-081X, Vol. 68, p. 89-100Article in journal (Refereed) Published
Abstract [en]

We consider a generalization of the classical Art Gallery Problem, where instead of a light source, the guards, called k-transmitters, model a wireless device with a signal that can pass through at most k walls. We show it is NP-hard to compute a minimum cover of point 2-transmitters, point k-transmitters, and edge 2-transmitters in a simple polygon. The point 2-transmitter result extends to orthogonal polygons. In addition, we give necessity and sufficiency results for the number of edge 2-transmitters in general, monotone, orthogonal monotone, and orthogonal polygons.

Place, publisher, year, edition, pages
Elsevier, 2018. Vol. 68, p. 89-100
Keywords [en]
Art Gallery Problem, 2-Transmitter, k-Transmitter, NP-hardness
National Category
Computer Sciences
Identifiers
URN: urn:nbn:se:liu:diva-142557DOI: 10.1016/j.comgeo.2017.06.004ISI: 000415778300008Scopus ID: 2-s2.0-85020645869OAI: oai:DiVA.org:liu-142557DiVA, id: diva2:1153802
Note

Funding agencies: AMS

Available from: 2017-10-31 Created: 2017-10-31 Last updated: 2019-01-25Bibliographically approved

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Schmidt, Christiane

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