A 2-packing set for an undirected graph $G=(V,E)$ is a subset $\mathcal{S} \subset V$ such that any two vertices $v_1,v_2 \in \mathcal{S}$ have no common neighbors. Finding a 2-packing set of maximum cardinality is a NP-hard problem. We develop a new approach to solve this problem on arbitrary graphs using its close relation to the independent set problem. Thereby, our algorithm red2pack uses new data reduction rules specific to the 2-packing set problem as well as a graph transformation. Our experiments show that we outperform the state-of-the-art for arbitrary graphs with respect to solution quality and also are able to compute solutions multiple orders of magnitude faster than previously possible. For example, we are able to solve 63% of our graphs to optimality in less than a second while the competitor for arbitrary graphs can only solve 5% of the graphs in the data set to optimality even with a 10 hour time limit. Moreover, our approach can solve a wide range of large instances that have previously been unsolved.

翻译：对于无向图$G=(V,E)$，2-包装集定义为子集$\mathcal{S} \subset V$，其中任意两个顶点$v_1,v_2 \in \mathcal{S}$均无公共邻接点。寻找最大基数2-包装集是NP-难问题。我们基于该问题与独立集问题的密切联系，提出一种适用于任意图的新求解方法。由此开发的算法red2pack采用了专门针对2-包装集问题的新数据归约规则，并结合图变换技术。实验表明，该方法在解质量上超越现有任意图最优算法，且计算速度相较此前方法提升数个数量级。例如，我们能在1秒内求解数据集中63%的图至最优解，而任意图竞争算法即使设置10小时时间限制，也仅能求解5%的图。此外，该方法可解决此前无法处理的广泛大规模实例。