We study the approximability of an existing framework for clustering edge-colored hypergraphs, which is closely related to chromatic correlation clustering and is motivated by machine learning and data mining applications where the goal is to cluster a set of objects based on multiway interactions of different categories or types. We present improved approximation guarantees based on linear programming, and show they are tight by proving a matching integrality gap. Our results also include new approximation hardness results, a combinatorial 2-approximation whose runtime is linear in the hypergraph size, and several new connections to well-studied objectives such as vertex cover and hypergraph multiway cut.

翻译：我们研究了现有边染色超图聚类框架的近似性，该框架与色相关聚类密切相关，并受机器学习和数据挖掘应用的驱动——其目标是根据不同类别或类型的多路交互来聚类对象集合。我们提出了基于线性规划的改进近似保证，并通过证明匹配的完整性间隙表明其紧性。我们的结果还包括新的近似难度结论、一种运行时间与超图规模呈线性关系的组合2-近似算法，以及与顶点覆盖、超图多路割等经典目标的新联系。