发表机构
İzmir Bakırçay University（伊兹密尔巴克尔恰伊大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究解决了20余年的Model-RB基准frb100-40的最大独立集与最小顶点覆盖问题，给出最优性证明，经预注册实验评估未发现新增算子或对比求解器的启发式优势。
AI 中文摘要
超过20年来，Model-RB基准测试frb100-40一直是公开的挑战；自2014年起，其公开记录停留在100个变量中的99个。我们为其4000顶点的图提供了一个可直接验证的100顶点独立集，结合经验证的100个大小为40的团划分，该证明表明最大独立集大小为100，最小顶点覆盖大小为3900。找到该证明的随机运行与该证明本身相互独立。我们在包含8668次有效运行的预注册实验中评估了其新增的二元和三元修复算子。主要比较发现，其相较于基础ULSA无可检测加速（风险比为0.967，95%置信区间为0.915-1.023；p=0.248），因子消融实验得出相同结论。在较小的FRB套件上，group-aware CSP流水线在2500次运行中全部求解，而LibMVC-NuMVC为2391/2500次。在frb100-40上，完整ULSA、基础ULSA和NuMVC各产生0/56个新证明。因无事件，计划的跨求解器风险比仍未确定。NuMVC在40次运行中最终覆盖大小为3902，16次运行中为3903。穷举枚举显示，108个唯一记录的冲突二状态中，无一个在汉明半径3内有严格改进的group-aware CSP邻域。该证明解决了该实例，实验明确了搜索障碍，预注册比较显示无启发式优势。
英文摘要
For more than 20 years, the Model-RB benchmark frb100-40 remained an open challenge; since 2014, its public record had stood at 99 of 100 variables. We give a directly checkable 100-vertex independent set for its 4,000-vertex graph. Together with a verified partition into 100 cliques of size 40, the witness proves that the maximum independent-set size is 100 and the minimum vertex-cover size is 3,900. The stochastic run that found the witness is kept separate from this proof. We evaluated its added pair and triple repair operators in a preregistered campaign comprising 8,668 valid runs. The primary comparison found no detectable acceleration over base ULSA (hazard ratio 0.967, 95% confidence interval 0.915-1.023; p=0.248), and the factorial ablation reached the same conclusion. On a smaller FRB suite, the group-aware CSP pipeline solved 2,500/2,500 runs, compared with 2,391/2,500 for LibMVC-NuMVC. On frb100-40, full ULSA, base ULSA, and NuMVC each produced 0/56 new certificates. With no events, the planned cross-solver hazard ratios remain unidentified. NuMVC ended with cover size 3,902 in 40 runs and 3,903 in 16. Exhaustive enumeration showed that none of the 108 unique recorded conflict-two states had a strictly improving group-aware CSP neighbor within Hamming radius three. The certificate settles the instance. The experiments characterize the search barrier, and the preregistered comparisons show no heuristic advantage.
Comments7 pages, 4 figures, 4 tables. Reproducibility artifact: https://doi.org/10.5281/zenodo.22257064
