Half-Guarding Weakly-Visible Polygons and Terrains

Authors

Nandhana Duraisamy, PSG College of Technology
Hannah Miller Hillberg, University of Wisconsin Oshkosh
Ramesh K. Jallu, Council of Indian Institutes of Information Technology
Erik Krohn, University of Wisconsin Oshkosh
Anil Maheshwari, Carleton University
Subhas C. Nandy, Indian Statistical Institute, Kolkata
Alex Pahlow, University of Wisconsin Oshkosh

Document Type

Conference Article

Publication Title

Leibniz International Proceedings in Informatics, LIPIcs

Abstract

We consider a variant of the art gallery problem where all guards are limited to seeing 180°. Guards that can only see in one direction are called half-guards. We give a polynomial time approximation scheme for vertex guarding the vertices of a weakly-visible polygon with half-guards. We extend this to vertex guarding the boundary of a weakly-visible polygon with half-guards. We also show NP-hardness for vertex guarding a weakly-visible polygon with half-guards. Lastly, we show that the orientation of half-guards is critical in terrain guarding. Depending on the orientation of the half-guards, the problem is either very easy (polynomial time solvable) or very hard (NP-hard).

DOI

10.4230/LIPIcs.FSTTCS.2022.18

Publication Date

12-1-2022

Recommended Citation

Duraisamy, Nandhana; Hillberg, Hannah Miller; Jallu, Ramesh K.; Krohn, Erik; Maheshwari, Anil; Nandy, Subhas C.; and Pahlow, Alex, "Half-Guarding Weakly-Visible Polygons and Terrains" (2022). Conference Articles. 371.
https://digitalcommons.isical.ac.in/conf-articles/371