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/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.