Opposing Half Guards
Erik Krohn, Bengt J. Nilsson, Christiane Schmidt
TL;DR
This paper investigates the art gallery problem with opposing half guards, providing new theorems, complexity results, and approximation algorithms for specific polygon classes.
Contribution
It introduces art gallery theorems for opposing half guards and demonstrates NP-hardness in monotone polygons, along with approximation algorithms for spiral and staircase polygons.
Findings
Location of half guards in 2-guardable polygons is unrestricted by extensions
NP-hardness of the problem in monotone polygons
Approximation algorithms for spiral and staircase polygons
Abstract
We study the art gallery problem for opposing half guards: guards that can either see to their left or to their right only. We present art gallery theorems, show that the location of half guards in 2-guardable polygons is not restricted to extensions, show that the problem is NP-hard in monotone polygons, and present approximation algorithms for spiral and staircase polygons.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Robotic Path Planning Algorithms