Implementation of polygon guarding algorithms for art gallery problems

TL;DR

This paper implements and compares existing polygon guarding algorithms for art gallery problems, and introduces a new algorithm that performs near optimally in experiments.

Contribution

The paper implements existing algorithms and proposes a new guard placement algorithm based on Ghosh's idea, demonstrating near-optimal results through experiments.

Findings

The new algorithm outperforms previous methods in guard efficiency.

Experimental results show near-optimal guard placement.

Comparison highlights strengths and weaknesses of each algorithm.

Abstract

Victor Klee introduce the art gallery problem during a conference in Stanford in August 1976 with that question: "How many guards are required to guard an art gallery?" In 1987, Ghosh provided an approximation algorithm for vertex guards problem that achieved $ O(\log n) $ approximation ratio. In 2017, Bhattacharya et. al presented an approximation algorithm for guarding weak visibility polygons. In our paper, we first implement these algorithms and then we test them for different types of polygons. We compare their performance in terms of number of guards used by them. In the last part, we have provided a new algorithm that uses Ghosh's idea. Experiments show that this algorithm assigns near optimal guards for guarding the input polygons.