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.
翻译:目前研究的目的是调查美术馆问题的一个特殊案例,即雕塑花园问题;在所述问题上,对于某个特定的多边形美元,最终目标是通过采用由卫兵组成的单调波林公式,确定内部多边形美元的最低保镖人数;正如调查结果所示,关于该问题的推测是,在最坏的情况下,要求卫兵用n-2美元来说明任何美元-硬币(Eppstein等人,2007年)。