K-SpecPart: A Supervised Spectral Framework for Multi-Way Hypergraph Partitioning Solution Improvement

State-of-the-art hypergraph partitioners follow the multilevel paradigm, constructing multiple levels of coarser hypergraphs to drive cutsize refinement. These partitioners face limitations: (i) coarsening processes depend on local neighborhood structure, ignoring global hypergraph structure; (ii) refinement heuristics risk entrapment in local minima. We introduce K-SpecPart, a supervised spectral framework addressing these limitations by solving a generalized eigenvalue problem, capturing balanced partitioning objectives and global hypergraph structure in a low-dimensional vertex embedding while leveraging high-quality multilevel partitioning solutions as hints. In multi-way partitioning, K-SpecPart derives multiple bipartitioning solutions from a multi-way hint partitioning solution. It integrates these solutions into the generalized eigenvalue problem to compute eigenvectors, creating a large-dimensional embedding. Linear Discriminant Analysis (LDA) is used to transform this into a lower-dimensional embedding. K-SpecPart constructs a family of trees from the vertex embedding and partitions them using a tree-sweeping algorithm. We extend SpecPart's tree partitioning algorithm for multi-way partitioning. The multiple tree-based partitioning solutions are overlaid, followed by lifting to a clustered hypergraph where an integer linear programming (ILP) partitioning problem is solved. Empirical studies show K-SpecPart's benefits. For bipartitioning, K-SpecPart outperforms SpecPart with improvements up to 30%. For multi-way partitioning, K-SpecPart surpasses hMETIS and KaHyPar, with improvements up to 20% in some cases.