A deterministic 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 − ε ) for any constant ε > 0. In this paper, we improve the approximation ratio to ( 0. 66835 − ε ). Furthermore, we can derandomize our algorithm.

Authors

• Jingyang Zhao
• Mingyu Xiao

Keywords

• Approximation algorithms
• Metric
• Triangle packing
• Cycle packing