Empty Rainbow Triangles in $k$-colored Point Sets

平面上彩色点集的彩虹多边形

Rainbow polygons for colored point sets in the plane

该研究针对平面彩色点集的完美彩虹多边形最小顶点数问题，确定了k≤7时的rb-index(k)值，给出k≥5时的上下界，并提出O(n log n)时间的构造算法。

一种在k色点集中识别彩虹正交凸4集的高效算法

An efficient algorithm for identifying rainbow ortho-convex 4-sets in k-colored point sets

研究判定k色平面点集是否存在四色点使其直角凸包面积为正的问题，通过象限等价转化提出最优的$O(n \log n)$时间算法并证明其下界。

最大宽度的彩虹平分空环形

Maximum-Width Rainbow-Bisecting Empty Annulus

研究平面上彩色点集的最大宽度彩虹平分空环形问题，提出了在特定时间与空间复杂度内计算轴平行正方形、矩形和圆形环形的高效算法。

A Note on Empty Balanced Tetrahedra in Two colored Point sets in $\mathbb{R}^3$

Let $S$ be a set of $n$ red and $n$ blue points in general position in $\mathbb{R}^3$. Let $τ$ be a tetrahedra with vertices on $S$. We say that $τ$ is \emph{empty} if it does not contain any point of $S$ in its interior. We say that $τ$ is \emph{balanced} if it contains two blue vertices and two red vertices. In this paper we show that $S$ spans $Ω(n^{5/2})$ empty balanced tetrahedra.