发表机构
Fudan University（复旦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对多级超图划分中收缩可能丢失最优解的问题，提出基于容量感知修复证书的认证安全粗化方法，证明其保留最优解并在电路基准上提升划分质量。
AI 中文摘要
多级划分器通过顶点收缩来缩小电路超图，然而，即使一次收缩满足块容量约束，仍可能消除所有最优的平衡二分。我们开发了认证安全粗化（CSC）方法，以识别在不计算最优解的情况下保留最优解的收缩。CSC 为任何分裂候选组的可行划分认证一个修复方案：该修复必须尊重固定的块容量，并且不得增加切割网目标。其界限排除了因容量约束而被迫切割的超边。成对证书检查单个合并，而有向最小割测试则认证那些仅在顶点一起移动时其节省才显现的组。我们证明，对于具有正整数顶点和网权重的超图，认证的不相交批次和带重新认证的连续轮次至少保留一个全局最优可行划分。在可精确求解实例上的实验证实了每个测试配置的最优保留；与 KaHyPar 集成降低了电路基准上每个实例最佳切割的总和，但增加了运行时间。
英文摘要
Multilevel partitioners shrink circuit hypergraphs through vertex contractions, yet a contraction that satisfies block capacity can still eliminate every optimal balanced bipartition. We develop certified safe coarsening (CSC) to identify contractions that preserve an optimum without computing that optimum. CSC certifies a repair for any feasible partition that splits a candidate group: the repair must respect the fixed block capacities and must not increase the cut-net objective. Its bounds exclude hyperedges that capacity constraints force to be cut. A pair certificate checks individual merges, while a directed minimum-cut test certifies groups whose savings emerge only when vertices move together. We prove that certified disjoint batches and successive rounds with recertification retain at least one globally optimal feasible partition for hypergraphs with positive integer vertex and net weights. Experiments on exactly solvable instances confirm optimum preservation for every tested configuration; integration with KaHyPar lowers the sum of per-instance best cuts on circuit benchmarks, with additional runtime.
