An Improved Approximation Algorithm for Metric Triangle Packing

Given an edge-weighted metric complete graph with $n$ vertices, the maximum weight metric triangle packing problem is to find a set of $n\mathrm{/}3$ 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 $(0.66768-\epsilon )$ for any constant $\epsilon >0$. In this paper, we improve the approximation ratio to $(0.66835-\epsilon )$. Furthermore, we can derandomize our algorithm.