HyperEF 2.0: Spectral Hypergraph Coarsening via Krylov Subspace Expansion and Resistance-based Local Clustering
Hamed Sajadinia, Zhuo Feng
TL;DR
HyperEF 2.0 tackles scalable spectral coarsening of large hypergraphs by leveraging effective resistances and an enhanced Krylov subspace approach to better approximate hyperedge connectivity. It couples a resistance-based local clustering refinement with a multilevel partitioning workflow, enabling higher-quality partitions and faster runtimes. The key contributions are the mixed star/clique Krylov expansion for more accurate resistance estimation, a local clustering refinement to improve balance and conductance, and seamless integration into a robust multilevel hypergraph partitioner that achieves state-of-the-art results on real-world VLSI benchmarks. Empirical results show improved conductance and significantly smaller partition cuts compared to state-of-the-art methods, alongside notable speedups over flow-based local clustering baselines.
Abstract
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 4.5x speedup over the latest flow-based local clustering algorithm, HyperSF, demonstrating both superior efficiency and partitioning quality.