An FPRAS for Two Terminal Reliability in Directed Acyclic Graphs

Authors Weiming Feng , Heng Guo

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Author Details

Weiming Feng
  • Institute for Theoretical Studies, ETH Zürich, Switzerland
Heng Guo
  • School of Informatics, University of Edinburgh, UK


We thank Kuldeep S. Meel for bringing the problem to our attention, Antoine Amarilli for explaining their method to us, and Marcelo Arenas for insightful discussions. We also thank Zongchen Chen for suggesting a better presentation of Theorem 1, and Mark Jerrum for some useful insights. This work was done in part while Weiming Feng was visiting the Simons Institute for the Theory of Computing.

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Weiming Feng and Heng Guo. An FPRAS for Two Terminal Reliability in Directed Acyclic Graphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 62:1-62:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


We give a fully polynomial-time randomized approximation scheme (FPRAS) for two terminal reliability in directed acyclic graphs (DAGs). In contrast, we also show the complementing problem of approximating two terminal unreliability in DAGs is #BIS-hard.

Subject Classification

ACM Subject Classification
  • Networks → Network reliability
  • Mathematics of computing → Approximation algorithms
  • Theory of computation → Generating random combinatorial structures
  • Approximate counting
  • Network reliability
  • Sampling algorithm


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