State-of-the-art hypergraph partitioners utilize a multilevel paradigm to construct progressively coarser hypergraphs across multiple layers, guiding cut refinements at each level of the hierarchy. Traditionally, these partitioners employ heuristic methods for coarsening and do not consider the structural features of hypergraphs. In this work, we introduce a multilevel spectral framework, SHyPar, for partitioning large-scale hypergraphs by leveraging hyperedge effective resistances and flow-based community detection techniques. Inspired by the latest theoretical spectral clustering frameworks, such as HyperEF and HyperSF, SHyPar aims to decompose large hypergraphs into multiple subgraphs with few inter-partition hyperedges (cut size). A key component of SHyPar is a flow-based local clustering scheme for hypergraph coarsening, which incorporates a max-flow-based algorithm to produce clusters with substantially improved conductance. Additionally, SHyPar utilizes an effective resistance-based rating function for merging nodes that are strongly connected (coupled). Compared with existing state-of-the-art hypergraph partitioning methods, our extensive experimental results on real-world VLSI designs demonstrate that SHyPar can more effectively partition hypergraphs, achieving state-of-the-art solution quality.

This paper introduces HyperEF 2.0, a scalable framework for spectral coarsening and clustering of large-scale hypergraphs through hyperedge effective resistances, aiming to decompose hypergraphs into multiple node clusters with a small number of inter-cluster hyperedges. Building on the recent HyperEF framework, our approach offers three primary contributions. Specifically, first, by leveraging the expanded Krylov subspace exploiting both clique and star expansions of hyperedges, we can significantly improve the approximation accuracy of effective resistances. Second, we propose a resistance-based local clustering scheme for merging small isolated nodes into nearby clusters, yielding more balanced clusters with substantially improved conductance. Third, the proposed HyperEF 2.0 enables the integration of resistance-based hyperedge weighting and community detection into a multilevel hypergraph partitioning tool, achieving state-of-the-art performance. Extensive experiments on real-world VLSI benchmarks show that HyperEF 2.0 can more effectively coarsen hypergraphs without compromising their structural properties, while delivering much better solution quality (e.g. conductance) than the state-of-the-art hypergraph coarsening methods, such as HyperEF and HyperSF. Moreover, compared to leading hypergraph partitioners such as hMETIS, SpecPart, MedPart, and KaHyPar, our framework consistently achieves smaller cut sizes. In terms of runtime, HyperEF 2.0 attains up to a 4.5× speedup over the latest flow-based local clustering algorithm, HyperSF, demonstrating both superior efficiency and partitioning quality.