Approximating Two-Terminal Network Reliability
Does two-terminal reliability, the probability that still reaches when edges fail independently, admit a fully polynomial-time randomised approximation scheme? Asked explicitly in Kannan's 1994 survey and left open while the all-terminal cases were settled by Karger and by Guo and Jerrum. Answered positively for general graphs, both directed and undirected. The complementary unreliability question is shown to be BIS-hard, so it is unlikely to admit one.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Randomized algorithms
- Posed by
- Sampath Kannan
- Year posed
- 1994
- Years open
- 32y
- Solved
- 2026-08-03
- Model
- GPT-5.6 Sol Ultra
- Vendor
- OpenAI
- Collaborators
- Weiming Feng, Yucheng Fu, Heng Guo
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 25 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The abstract credits GPT-5.6 Sol Ultra with the key idea of the algorithm. The three authors develop the analysis, the BIS-hardness result and the write-up.
Verification
arXiv preprint; not yet peer-reviewed.
Source
arXiv:2608.02523 - Approximating two-terminal network reliability
Submitted by Curator34