An Approximation Algorithm for the Art Gallery Problem

  title={An Approximation Algorithm for the Art Gallery Problem},
  author={{\'E}douard Bonnet and Tillmann Miltzow},
  booktitle={International Symposium on Computational Geometry},
Given a simple polygon $\mathcal{P}$ on $n$ vertices, two points $x,y$ in $\mathcal{P}$ are said to be visible to each other if the line segment between $x$ and $y$ is contained in $\mathcal{P}$. The Point Guard Art Gallery problem asks for a minimum set $S$ such that every point in $\mathcal{P}$ is visible from a point in $S$. The set $S$ is referred to as guards. Assuming integer coordinates and a specific general position assumption, we present the first $O(\log \text{OPT})$-approximation… 

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