On the Complexity of Half-Guarding Monotone Polygons

TL;DR

This paper studies a specialized art gallery problem variant with half-guards in monotone polygons, offering improved approximation algorithms and establishing NP-hardness results for the problem.

Contribution

It introduces a polynomial-time approximation algorithm with an improved ratio and proves NP-hardness for point guarding with half-guards in monotone polygons.

Findings

Improved approximation ratio from 40 to 8.

Established NP-hardness of the problem.

Provided polynomial-time approximation algorithm.

Abstract

We consider a variant of the art gallery problem where all guards are limited to seeing to the right inside a monotone polygon. We call such guards: half-guards. We provide a polynomial-time approximation for point guarding the entire monotone polygon. We improve the best known approximation of 40 from [11], to 8. We also provide an NP-hardness reduction for point guarding a monotone polygon with half-guards.