What was already known
An approximation scheme was known for directed acyclic graphs. The general directed and undirected two-terminal problem had remained open since at least Kannan’s 1994 survey.
AI involvement
A GPT-5.6 Sol Ultra run prompted by Fu proposed a Markov-chain approach, including retained annealing and flow-analysis ideas. Feng, Fu and Guo verified, simplified and strengthened it and wrote the final proofs.
Two decisive algorithmic ideas are explicitly retained from the model run, within a human-designed search and human-written final analysis.
Importance
Answers a longstanding approximate-counting question for general network reliability.
Limitations
The separate unreliability hardness result is human-attributed. The final chain, running-time bound and proofs are human revisions of the model proposal; the long model run is not public.
Technical verification
The authors explicitly report verifying the model algorithm and Markov chain and writing the complete proof of the final FPRAS. This is a reported human check, not a reproduced complexity audit.
Independent checking
Author verification and simplification of model algorithm and chain, followed by author-written proofs
- Checker
- Weiming Feng, Yucheng Fu and Heng Guo, authors
- Scope
- Directed two-terminal FPRAS, including annealing and flow-based chain analysis
- Basis
- Reported by the linked checker
Human understanding
The authors explain the annealing distributions, chain, flow congestion and reduction to undirected reliability.
Correction and publication history
Answers a longstanding approximate-counting question for general network reliability.
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