A Polynomial-Time Approximation Algorithm for All-Terminal Network Reliability

Authors Heng Guo , Mark Jerrum

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Heng Guo
  • School of Informatics, University of Edinburgh, Informatics Forum, Edinburgh, EH8 9AB, United Kingdom.
Mark Jerrum
  • School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London, E1 4NS, United Kingdom.

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Heng Guo and Mark Jerrum. A Polynomial-Time Approximation Algorithm for All-Terminal Network Reliability. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 68:1-68:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Generating random combinatorial structures
  • Approximate counting
  • Network Reliability
  • Sampling
  • Markov chains


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