Lower Bound for Sculpture Garden Problem

Marzieh Eskandari, Bahram Sadeghi Bigham

The purpose of the current study is to investigate a special case of art gallery problem, namely Sculpture Garden Problem. In the said problem, for a given polygon $P$, the ultimate goal is to place the minimum number of guards to define the interior polygon $P$ by applying a monotone Boolean formula composed of the guards. As the findings indicate, the conjecture about the issue that in the worst case, $n-2$ guards are required to describe any $n$-gon (Eppstein et al. 2007) can be conclusively proved.

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