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arXiv · 1709.08561

A polynomial-time approximation algorithm for all-terminal network reliability

Heng Guo·Mark Jerrum
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Abstract

We give a fully polynomial-time randomized approximation scheme (FPRAS) for the all-terminal network reliability problem, which is to determine the probability that, in a undirected graph, assuming each edge fails independently, the remaining graph is still connected. Our main contribution is to confirm a conjecture by Gorodezky and Pak (Random Struct. Algorithms, 2014), that the expected running time of the "cluster-popping" algorithm in bi-directed graphs is bounded by a polynomial in the size of the input.

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Heng Guo, Mark Jerrum. 2017-09-25. A polynomial-time approximation algorithm for all-terminal network reliability. https://doi.org/10.1137/18m1201846

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