HyperEF: Spectral Hypergraph Coarsening by Effective-Resistance Clustering

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...

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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
ISSN:1558-2434
DOI:10.1145/3508352.3549438