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 $G=(V,E)$，2-包装集是子集 $\mathcal{S} \subset V$，其中任意两个顶点 $v_1,v_2 \in \mathcal{S}$ 没有公共邻居。寻找基数最大的2-包装集是一个NP难问题。我们利用其与独立集问题的紧密关系，开发了一种在任意图上求解该问题的新方法。具体而言，我们的算法red2pack采用了针对2-包装集问题的新数据约简规则以及图变换技术。实验表明，与现有最优算法相比，我们在任意图上的解质量方面表现更优，并且计算速度比先前可能的方法快多个数量级。例如，我们能在不到一秒内将测试数据集中63%的图最优求解，而针对任意图的竞争算法即使设置10小时的时间限制，也仅能最优求解其中5%的图。此外，我们的方法能够求解之前无法解决的广泛大规模实例。