A Multi-Level Framework for Multi-Objective Hypergraph Partitioning: Combining Minimum Spanning Tree and Proximal Gradient

2025-09-26

AI Summary

This work addresses two key challenges in multi-objective hypergraph partitioning: susceptibility to local optima and insufficient vertex feature diversity. Methodologically, we propose a novel partitioning framework based on nonconvex constraint relaxation and proximal gradient optimization. Our approach integrates an accelerated proximal gradient algorithm with a Prim-built minimum spanning tree (MST), enabling a hierarchical partitioning strategy and recursive MST-based clustering. Key techniques—including vertex subset sampling, greedy migration, and swap-based refinement—are incorporated to enhance partition quality. Experiments on public benchmarks show that our method reduces cut edge count by 2–5% over KaHyPar, with gains up to 35% on specific instances; it also outperforms hMetis on weighted vertex sets and achieves up to 16% improvement when refining hMetis solutions. The core contribution lies in the first synergistic integration of MST-guided structure learning and nonconvex proximal optimization for hypergraph partitioning, significantly improving both feature diversity and global partitioning capability.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Non-convex Optimization
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Web Mining and Content Analysis: Bridging structured and unstructured data

Abstract

This paper proposes an efficient hypergraph partitioning framework based on a novel multi-objective non-convex constrained relaxation model. A modified accelerated proximal gradient algorithm is employed to generate diverse $k$-dimensional vertex features to avoid local optima and enhance partition quality. Two MST-based strategies are designed for different data scales: for small-scale data, the Prim algorithm constructs a minimum spanning tree followed by pruning and clustering; for large-scale data, a subset of representative nodes is selected to build a smaller MST, while the remaining nodes are assigned accordingly to reduce complexity. To further improve partitioning results, refinement strategies including greedy migration, swapping, and recursive MST-based clustering are introduced for partitions. Experimental results on public benchmark sets demonstrate that the proposed algorithm achieves reductions in cut size of approximately 2%--5% on average compared to KaHyPar in 2, 3, and 4-way partitioning, with improvements of up to 35% on specific instances. Particularly on weighted vertex sets, our algorithm outperforms state-of-the-art partitioners including KaHyPar, hMetis, Mt-KaHyPar, and K-SpecPart, highlighting its superior partitioning quality and competitiveness. Furthermore, the proposed refinement strategy improves hMetis partitions by up to 16%. A comprehensive evaluation based on virtual instance methodology and parameter sensitivity analysis validates the algorithm's competitiveness and characterizes its performance trade-offs.

Problem

• Proposes multi-objective hypergraph partitioning framework
• Combines minimum spanning tree with proximal gradient
• Improves partitioning quality and reduces cut size

Innovation

• Multi-objective hypergraph partitioning with non-convex relaxation
• Accelerated proximal gradient generates diverse vertex features
• MST-based strategies and refinement for different data scales