SHyPar: A Spectral Coarsening Approach to Hypergraph Partitioning

TL;DR

SHyPar introduces a spectral multilevel hypergraph partitioning framework that leverages effective resistances and flow-based clustering to improve partition quality on large-scale hypergraphs, especially in VLSI design.

Contribution

It proposes a novel spectral coarsening method using flow-based clustering and effective resistance, advancing hypergraph partitioning techniques beyond heuristic approaches.

Findings

Achieves state-of-the-art partition quality on real-world VLSI hypergraphs.

Utilizes flow-based clustering for better hypergraph coarsening.

Demonstrates significant improvements over existing methods.

Abstract

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.