We study the problem of minimum enclosing rectangle with outliers, which asks to find, for a given set of $n$ planar points, a rectangle with minimum area that encloses at least $(n-t)$ points. The uncovered points are regarded as outliers. We present an exact algorithm with $O(kt^3+ktn+n^2\log n)$ runtime, assuming that no three points lie on the same line. Here $k$ denotes the number of points on the first $(t+1)$ convex layers. We further propose a sampling algorithm with runtime $O(n+\mbox{poly}(\log{n}, t, 1/\epsilon))$, which with high probability finds a rectangle covering at least $(1-\epsilon)(n-t)$ points with at most the exact optimal area.

翻译：我们研究的是将最小值与外部值连接在一起的问题。 外部值要求找到一个最小值区域的矩形, 其中至少包含$( n- t) 点。 所发现的点被视为外部值。 我们用$( kt}3+ktn+n ⁇ 2\log n) 运行时算出一个精确的算法, 假设线上没有三点。 这里的美元表示第一个 $( t+1) 方形层的点数。 我们进一步建议使用运行时 $( n ⁇ box{poly} (\log{ t, 1/\ epsilon) 值的抽样算法, 极有可能找到至少 $( 1-\ epsilon) (n- t) 点数, 且最符合最佳区域 。