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 the graphs in the tested data set to optimality in less than a second while the competitor for arbitrary graphs can only solve 5% of these graphs 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$G=(V,E)$，一个2-填充集是子集$\mathcal{S} \subset V$，使得任意两个顶点$v_1,v_2 \in \mathcal{S}$没有公共邻居。寻找最大基数2-填充集是一个NP难问题。我们利用其与独立集问题的密切联系，提出了一种在任意图上解决该问题的新方法。由此，我们的算法red2pack采用了针对2-填充集问题的新数据归约规则以及图变换技术。实验表明，我们在解质量上超越了现有任意图上的最优方法，并且计算速度比先前可能的方法快数个数量级。例如，我们在不到一秒内即可将测试数据集中的63%的图精确求解，而针对任意图的竞争方法即便在10小时时间限制下也仅能精确求解其中5%的图。此外，我们的方法能够求解大量先前未能解决的规模较大的实例。