HyperEF: Spectral Hypergraph Coarsening by Effective-Resistance Clustering

• Published in: 2022 IEEE/ACM International Conference On Computer Aided Design (ICCAD) pp. 1 - 9
• Main Authors: Aghdaei, Ali, Feng, Zhuo
• Format: Conference Proceeding
• Language: English
• Published: ACM 29.10.2022
• Subjects: Clustering algorithms; Clustering methods; Design automation; effective resistance; Estimation; graph clustering; hypergraph coarsening; Resistance; Runtime; Scalability; spectral graph theory
• ISSN: 1558-2434
• DOI: 10.1145/3508352.3549438

This paper introduces a scalable algorithmic framework (HyperEF) for spectral coarsening (decomposition) of large-scale hypergraphs by exploiting hyperedge effective resistances. Motivated by the latest theoretical framework for low-resistance-diameter decomposition of simple graphs, HyperEF aims at decomposing large hypergraphs into multiple node clusters with only a few inter-cluster hyperedges. The key component in HyperEF is a nearly-linear time algorithm for estimating hyperedge effective resistances, which allows incorporating the latest diffusion-based non-linear quadratic operators defined on hypergraphs. To achieve good runtime scalability, HyperEF searches within the Krylov subspace (or approximate eigensubspace) for identifying the nearly-optimal vectors for approximating the hyperedge effective resistances. In addition, a node weight propagation scheme for multilevel spectral hypergraph decomposition has been introduced for achieving even greater node coarsening ratios. When compared with state-of-the-art hypergraph partitioning (clustering) methods, extensive experiment results on real-world VLSI designs show that HyperEF can more effectively coarsen (decompose) hypergraphs without losing key structural (spectral) properties of the original hypergraphs, while achieving over 70× runtime speedups over hMetis and 20× speedups over HyperSF.