Given an edge-weighted metric complete graph with $n$ vertices, the maximum weight metric triangle packing problem is to find a set of $n/3$ vertex-disjoint triangles with the total weight of all triangles in the packing maximized. Several simple methods can lead to a 2/3-approximation ratio. However, this barrier is not easy to break. Chen et al. proposed a randomized approximation algorithm with an expected ratio of $(0.66768-\varepsilon)$ for any constant $\varepsilon>0$. In this paper, we improve the approximation ratio to $(0.66835-\varepsilon)$. Furthermore, we can derandomize our algorithm.

翻译：给定一个具有$n$个顶点的边赋权度量完全图，最大权度量三角形打包问题旨在寻找$n/3$个顶点互不相交的三角形，使得打包中所有三角形的总权重最大化。几种简单方法可实现2/3的近似比，然而这一界限不易突破。Chen等人提出一种随机化近似算法，对于任意常数$\varepsilon>0$，其期望近似比为$(0.66768-\varepsilon)$。本文将该近似比改进为$(0.66835-\varepsilon)$，此外我们还可以对算法进行去随机化处理。