In this paper, we study two extensions of the maximum bichromatic separating rectangle (MBSR) problem introduced in \cite{Armaselu-CCCG, Armaselu-arXiv}. One of the extensions, introduced in \cite{Armaselu-FWCG}, is called \textit{MBSR with outliers} or MBSR-O, and is a more general version of the MBSR problem in which the optimal rectangle is allowed to contain up to $k$ outliers, where $k$ is given as part of the input. For MBSR-O, we improve the previous known running time bounds of $O(k^7 m \log m + n)$ to $O(k^3 m + m \log m + n)$. The other extension is called \textit{MBSR among circles} or MBSR-C and asks for the largest axis-aligned rectangle separating red points from blue unit circles. For MBSR-C, we provide an algorithm that runs in $O(m^2 + n)$ time.

翻译：在本文中,我们研究了在\ cite{ Armaslu-CCCG, Armaslu-arXiv} 中引入的最大双色分离矩形(MBSR)问题的两个延伸。 在\ cite{Armaslu-FWCG} 中引入的一个扩展名为\ textit{MBSR with extliers} 或 MBSR-O, 是MBSR问题的一个更普通的版本, 允许最佳矩形包含最多为$k$的外端, 以美元作为输入的一部分。 对于 MBSR- O, 我们将已知的$( kä7 m log m + n) 的运行时间范围改进为$( kä3 m + m log m + n) $( k) 。 另一个扩展名为\ textitit{MBSR- C 或 MBSR- C, 并请求使用最大轴- 轴矩形红点分隔于蓝色单元圈的红点。 对于 MBSR- C, 我们提供一种以 $ time.