A deterministic approximation algorithm for metric triangle packing

Jingyang Zhao, Mingyu Xiao

Abstract: 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−ε) for any constant ε>0. In this paper, we improve the approximation ratio to (0.66835−ε). Furthermore, we can derandomize our algorithm.