arXiv：cs.LG· M. Harper Langston, Pierre-David Letourneau, Dalton Jones, Harris Teague, Peter Scott, Mingu Lee, Richard Lethin, Chris Lott, Roland Memisevic, Fatih Porikli·· 3 小时前
图粗化让计算受限的非凸 MAX-CUT 逃离局部最优
Graph Coarsening Enables Escaping Local Optima in Compute-Constrained Nonconvex MAX-CUT
AI 导读
研究提出以 Particle Polynomial Relaxation（PPR）求解 MAX-CUT，并用谱图粗化方法 Combinatorial Multigrid（CMG）做热启动，在 t2g20（n=400）上平均达到最优解的 97.5%、最佳运行 98.4%。
正文
Abstract:Because its binary optimization landscape contains exponentially many local optima, MAX-CUT is highly sensitive to initialization. We study Particle Polynomial Relaxation (PPR), a moment-based nonconvex continuous reformulation possessing an advantageous optimization landscape. We warm-start PPR with Combinatorial Multigrid (CMG), a spectral graph-coarsening method that produces structure-aware initial solutions in near-linear time without training data. On \texttt{t2g20} ($n=400$), benchmark instance with known exact optimum, the combined CMG+PPR pipeline reaches $97.5\%$ of optimum on average and $98.4\%$ on the best run. An extended variant with discrete local-search refinement reaches the published optimum on all sixty Biq Mac instances evaluated by a recent neural branch-and-bound method. Using a sparse CSR representation, the same approach scales to G-set instances with up to $20{,}000$ vertices reducing memory requirements by up to $3333\times$ while maintaining a consistent improvement over the CMG warm start. Gains are largest on sparse weighted graphs; on dense graphs we complement the pipeline with spectral sparsification.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computation and Language (cs.CL); Numerical Analysis (math.NA); Optimization and Control (math.OC) |
| Cite as: | arXiv:2610.19043 [cs.LG] |
| (or arXiv:2610.19043v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.19043 arXiv-issued DOI via DataCite (pending registration) |
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| Journal reference: | OPT2026 (Neurips Workshop) |
Submission history
From: M. Harper Langston [view email]
[v1]
Tue, 13 Oct 2026 18:32:31 UTC (1,689 KB)
来源：arXiv：cs.LG · arxiv.org