SIAM Journal on Computing, Volume 50, Issue 1, Page 145-170, January 2021.
Let $P$łabelpage1 be a set of $n$ points in the plane. We consider a variation of the classical Erdös--Szekeres problem, presenting efficient algorithms with $O(n^3)$ running time and $O(n^2)$ space complexity that compute (1) a subset $S$ of $P$ such that the boundary of the rectilinear convex hull of $S$ has the maximum number of points from $P$, (2) a subset $S$ of $P$ such that the boundary of the rectilinear convex hull of $S$ has the maximum number of points from $P$ and its interior contains no element of $P$, (3) a subset $S$ of $P$ such that the rectilinear convex hull of $S$ has maximum area and its interior contains no element of $P$, and (4) when each point of $P$ is assigned a weight, positive or negative, a subset $S$ of $P$ that maximizes the total weight of the points in the rectilinear convex hull of $S$. We also revisit the problems of computing a maximum area orthoconvex polygon and computing a maximum area staircase polygon, amidst a point set in a rectangular domain. We obtain new and simpler algorithms to solve both problems with the same complexity as in the state of the art.

中文翻译：

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最大直线凸子集

SIAM Journal on Computing，第 50 卷，第 1 期，第 145-170 页，2021 年 1 月。
令 $P$łabelpage1 是平面上的一组 $n$ 点。我们考虑经典 Erdös--Szekeres 问题的变体，提出具有 $O(n^3)$ 运行时间和 $O(n^2)$ 空间复杂度的高效算法，计算 (1) $ 的子集 $S$ P$使得$S$的直线凸包的边界具有来自$P$的最大点数，(2)$P$的子集$S$使得$S的直线凸包的边界$具有来自$P$的最大点数并且其内部不包含$P$的元素，(3)$P$的子集$S$使得$S$的直线凸包具有最大面积并且其内部不包含 $P$ 的元素，并且 (4) 当 $P$ 的每个点都被分配了一个权重，无论是正的还是负的，$P$ 的一个子集 $S$ 使直线凸包中的点的总权重最大化$S$。我们还重新讨论了在矩形域中的点集内计算最大面积正凸多边形和计算最大面积阶梯多边形的问题。我们获得了新的、更简单的算法，以与现有技术相同的复杂性来解决这两个问题。