A PTAS for vertex guarding weakly-visible polygons - An extended abstract

TL;DR

This paper introduces a Polynomial-Time Approximation Scheme (PTAS) for efficiently approximating the minimum vertex guard set in weakly-visible polygons, improving solutions for guarding problems in computational geometry.

Contribution

It provides the first PTAS for vertex guarding weakly-visible polygons and extends this to boundary guarding, advancing approximation techniques in geometric guarding.

Findings

Developed a PTAS for vertex guarding weakly-visible polygons

Extended PTAS to boundary guarding of polygons

Achieved near-optimal guard set approximations in polynomial time

Abstract

In this extended abstract, we present a PTAS for guarding the vertices of a weakly-visible polygon $P$ from a subset of its vertices, or in other words, a PTAS for computing a minimum dominating set of the visibility graph of the vertices of $P$. We then show how to obtain a PTAS for vertex guarding $P$'s boundary.