An Improved Approximation Algorithm for Metric Triangle Packing
<|reference_start|>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.<|reference_end|>
@article{zhao2024an,
    title={An Improved Approximation Algorithm for Metric Triangle Packing},
    author={Jingyang Zhao and Mingyu Xiao},
    journal={arXiv preprint arXiv:2402.08216},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.08216},
    primaryClass={cs.DS}
}