Fast algorithms for edge coloring in clustered hypergraphs: A study of computational efficiency

The generalization of edge coloring in hypergraphs, especially clustered ones, remains an open problem due to the intricate structure and organization of hyper-edges grouped in clusters. This study addresses the computational challenges associated with edge coloring in clustered hypergraphs by introducing a novel suite of fast algorithms specifically designed to achieve improved accuracy and computation time. The algorithms utilize structural properties such as hypergraph Laplacian spectral features and submodular optimization to enhance efficiency. Experimental results demonstrate a 10-15% improvement in clustering accuracy and a 20% reduction in computational time compared to baseline methods, validating the approach for both synthetic and real-world datasets. These findings contribute to hypergraph theory and propose a practical solution for applications in network layout, parallel computing frameworks, and data organization. Future work could further optimize these algorithms for large-scale real-time applications.