We propose improved exact and heuristic algorithms for solving the maximum weight clique problem, a well-known problem in graph theory with many applications. Our algorithms interleave successful techniques from related work with novel data reduction rules that use local graph structure to identify and remove vertices and edges while retaining the optimal solution. We evaluate our algorithms on a range of synthetic and real-world graphs, and find that they outperform the current state of the art on most inputs. Our data reductions always produce smaller reduced graphs than existing data reductions alone. As a result, our exact algorithm, MWCRedu, finds solutions orders of magnitude faster on naturally weighted, medium-sized map labeling graphs and random hyperbolic graphs. Our heuristic algorithm, MWCPeel, outperforms its competitors on these instances, but is slightly less effective on extremely dense or large instances.

翻译：我们提出了求解最大权团问题（图论中一个具有广泛应用背景的著名问题）的改进精确算法与启发式算法。我们的算法融合了相关研究中成熟的技术与新颖的数据约简规则——这些规则利用局部图结构识别并移除顶点和边，同时保证最优解不变。我们在多种合成图和真实世界图上评估了所提算法，发现它们在大多数输入上超越了当前最优方法。与仅使用现有数据约简技术相比，我们的数据约简总能生成规模更小的约简图。因此，我们的精确算法MWCRedu在自然加权的中等规模地图标注图和随机双曲图上的求解速度提升了数个数量级。启发式算法MWCPeel在上述实例中优于竞争算法，但在极稠密或极大规模实例上的效果略逊一筹。