{"ID":2865315,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.22294","arxiv_id":"2509.22294","title":"A Multi-Level Framework for Multi-Objective Hypergraph Partitioning: Combining Minimum Spanning Tree and Proximal Gradient","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.","short_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-bas...","url_abs":"https://arxiv.org/abs/2509.22294","url_pdf":"https://arxiv.org/pdf/2509.22294v1","authors":"[\"Yingying Li\",\"Mingxuan Xie\",\"Hailong You\",\"Yongqiang Yao\",\"Hongwei Liu\"]","published":"2025-09-26T12:55:30Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.CO\"]","methods":"[]","has_code":false}