frb100-40 After Two Decades: An Optimality Certificate and a Preregistered Search Study
A directly checkable 100-vertex independent set is provided for the 4,000-vertex frb100-40 graph. A verified partition into 100 cliques of size 40 proves the maximum independent-set size is 100 and the minimum vertex-cover size is 3,900. A preregistered campaign of 8,668 valid runs found no detectable acceleration from added pair and triple repair operators over base ULSA (hazard ratio 0.967, 95% CI 0.915-1.023; p=0.248). On a smaller FRB suite, the group-aware CSP pipeline solved 2,500/2,500 runs versus 2,391/2,500 for LibMVC-NuMVC. On frb100-40, full ULSA, base ULSA, and NuMVC each produced 0/56 new certificates.
The paper resolves the 20-year-old frb100-40 benchmark by providing a verifiable 100-vertex independent set and a clique partition proving optimality. A preregistered study of 8,668 runs shows no significant improvement from added repair operators over base ULSA. The group-aware CSP pipeline outperforms LibMVC-NuMVC on a smaller FRB suite, but no solver produced new certificates on frb100-40.
The optimality certificate combines a constructive witness (independent set) with a dual bound (clique partition), a standard but effective approach for exact combinatorial optimization. The preregistered design with hazard ratios and confidence intervals provides rigorous evidence that the added repair operators do not improve runtime. The failure of all solvers to produce new certificates on frb100-40 suggests the benchmark remains computationally hard despite the known optimum.
This work demonstrates the value of formal verification and preregistered experiments in AI research, potentially influencing best practices for benchmarking and reproducibility. The group-aware CSP pipeline's superior performance on smaller instances may attract interest from industries using constraint satisfaction, such as scheduling, logistics, and hardware verification.
The certified solution and improved CSP pipeline could benefit companies needing reliable solutions to hard combinatorial problems, such as in resource allocation, network design, and verification. The emphasis on reproducibility and preregistration may enhance trust in AI research outputs for enterprise adoption.
Future work may focus on improving solver efficiency for large hard instances like frb100-40, possibly through novel heuristics or hybrid methods. The preregistered methodology could become more common in AI benchmarking. The availability of a certified optimum may enable new research on algorithm behavior near optimality.