A new metaheuristic approach for the art gallery problem

TL;DR

This paper introduces a novel metaheuristic approach using Particle Filter algorithms to efficiently approximate solutions for the NP-hard art gallery problem, achieving higher accuracy with fewer guards in complex polygons.

Contribution

It presents a new particle filter-based method for the art gallery problem, improving solution accuracy and efficiency over existing approaches.

Findings

More accurate guard placement with fewer guards

Effective resampling reduces runtime

Validated on complex random polygons

Abstract

In the problem "Localization and trilateration with the minimum number of landmarks", we faced the 3-Guard and classic Art Gallery Problems. The goal of the art gallery problem is to find the minimum number of guards within a simple polygon to observe and protect its entirety. It has many applications in robotics, telecommunications, etc. There are some approaches to handle the art gallery problem that is theoretically NP-hard. This paper offers an efficient method based on the Particle Filter algorithm which solves the most fundamental state of the problem in a nearly optimal manner. The experimental results on the random polygons generated by Bottino et al. \cite{bottino2011nearly} show that the new method is more accurate with fewer or equal guards. Furthermore, we discuss resampling and particle numbers to minimize the run time.