This work addresses the well-known Maximum Independent Set problem in the context of hypergraphs. While this problem has been extensively studied on graphs, we focus on its strong extension to hypergraphs, where edges may connect any number of vertices. A set of vertices in a hypergraph is strongly independent if there is at most one vertex per edge in the set. One application for this problem is to find perfect minimal hash functions. We propose nine new data reduction rules specifically designed for this problem. Our reduction routine can serve as a preprocessing step for any solver. We analyze the impact on the size of the reduced instances and the performance of several subsequent solvers when combined with this preprocessing. Our results demonstrate a significant reduction in instance size and improvements in running time for subsequent solvers. The preprocessing routine reduces instances, on average, to 22% of their original size in 6.76 seconds. When combining our reduction preprocessing with the best-performing exact solver, we observe an average speedup of 3.84x over not using the reduction rules. In some cases, we can achieve speedups of up to 53x. Additionally, one more instance becomes solvable by a method when combined with our preprocessing.

翻译：本研究针对超图背景下的经典最大独立集问题展开探讨。尽管该问题在图结构上已得到广泛研究，我们重点关注其在超图上的强扩展形式，其中超边可连接任意数量的顶点。超图中的顶点集合若满足每条超边中至多包含该集合中的一个顶点，则称为强独立集。该问题的一个应用场景是寻找完美最小哈希函数。我们针对此问题提出了九种新的数据约简规则。我们的约简程序可作为任意求解器的预处理步骤。通过分析约简后实例的规模变化以及结合该预处理后多种求解器的性能表现，实验结果表明实例规模显著减小且后续求解器的运行时间得到改善。预处理程序平均在6.76秒内将实例规模缩减至原始大小的22%。当将我们的约简预处理与性能最优的精确求解器结合时，相较于不使用约简规则的情况，平均可获得3.84倍的加速比。在某些案例中，加速比最高可达53倍。此外，结合我们的预处理后，某求解方法可多解决一个原本无法求解的实例。