The Generalized Independent Set (GIS) problem extends the classical maximum independent set problem by incorporating profits for vertices and penalties for edges. This generalized problem has been identified in diverse applications in fields such as forest harvest planning, competitive facility location, social network analysis, and even machine learning. However, solving the GIS problem in large-scale, real-world networks remains computationally challenging. In this paper, we explore data reduction techniques to address this challenge. We first propose 14 reduction rules that can reduce the input graph with rigorous optimality guarantees. We then present a reduction-driven local search (RLS) algorithm that integrates these reduction rules into the pre-processing, the initial solution generation, and the local search components in a computationally efficient way. The RLS is empirically evaluated on 278 graphs arising from different application scenarios. The results indicates that the RLS is highly competitive -- For most graphs, it achieves significantly superior solutions compared to other known solvers, and it effectively provides solutions for graphs exceeding 260 million edges, a task at which every other known method fails. Analysis also reveals that the data reduction plays a key role in achieving such a competitive performance.

翻译：广义独立集（GIS）问题通过引入顶点收益与边惩罚机制，拓展了经典最大独立集问题。该广义问题已在森林采伐规划、竞争性设施选址、社交网络分析乃至机器学习等多元领域得到应用验证。然而，在大规模真实世界网络中求解GIS问题仍面临计算挑战。本文通过探索数据约简技术应对该挑战：首先提出14项具有严格最优性保证的约简规则，可有效缩减输入图规模；继而提出约简驱动局部搜索（RLS）算法，以计算高效方式将这些约简规则集成至预处理、初始解生成及局部搜索三大组件。我们在来自不同应用场景的278张图上对RLS进行实证评估，结果表明该算法具有显著竞争力——对于大多数图，RLS所得解相较于已知求解器具有明显优势，且能有效处理包含超过2.6亿条边的图（当前已知方法均无法完成此任务）。分析进一步揭示，数据约简在实现如此优异性能中发挥着关键作用。