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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| Vydáno v: | 2022 IEEE/ACM International Conference On Computer Aided Design (ICCAD) s. 1 - 9 |
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| Jazyk: | angličtina |
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29.10.2022
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| ISSN: | 1558-2434 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Feng, Zhuo Aghdaei, Ali |
| Author_xml | – sequence: 1 givenname: Ali surname: Aghdaei fullname: Aghdaei, Ali email: aaghdae1@stevens.edu organization: Stevens Institute of Technology – sequence: 2 givenname: Zhuo surname: Feng fullname: Feng, Zhuo email: zhuo.feng@stevens.edu organization: Stevens Institute of Technology |
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| Snippet | This paper introduces a scalable algorithmic framework (HyperEF) for spectral coarsening (decomposition) of large-scale hypergraphs by exploiting hyperedge... |
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| SubjectTerms | Clustering algorithms Clustering methods Design automation effective resistance Estimation graph clustering hypergraph coarsening Resistance Runtime Scalability spectral graph theory |
| Title | HyperEF: Spectral Hypergraph Coarsening by Effective-Resistance Clustering |
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