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-包装集是顶点子集$\mathcal{S} \subset V$，满足任意两个顶点$v_1,v_2 \in \mathcal{S}$没有公共邻居。寻找最大基数2-包装集是NP难问题。我们利用其与独立集问题的密切关系，提出了一种在任意图上求解该问题的新方法。为此，我们的算法red2pack采用了针对2-包装集问题的新数据归约规则以及图变换技术。实验表明，在解质量上我们优于当前针对任意图的最先进方法，同时计算速度比先前方法快数个数量级。例如，我们能在不到一秒内求解63%的测试图至最优，而针对任意图的竞争方法即使设置10小时时间限制，也仅能求解数据集中5%的图至最优。此外，我们的方法能够求解大量先前无法求解的大规模实例。