Approximating Two-Terminal Network Reliability
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Statement
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.
Context
The approximability of two-terminal reliability was asked explicitly in Kannan's 1994 survey and stood while the neighbouring all-terminal problems fell to Karger and to Guo and Jerrum. The paper settles it in both the directed and undirected cases and pairs it with a hardness result for the complementary quantity.
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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.
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