### Abstract

We introduce classes of narrow graphs (including grid strips of fixed width), for which the graph reliability problem admits a polynomial time algorithm. Using this algorithm, we show that graph reliability is computable in polynomial time for the average complexity with respect to a Gaussian distribution. The latter is defined as follows: the vertices are numbered by integers {1,2, . . . n}, and the probability that an edge between i and j is present is e^{-|i-j|2}.

Original language | English (US) |
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Pages (from-to) | 307-315 |

Number of pages | 9 |

Journal | Fundamenta Informaticae |

Volume | 36 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1998 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Algebra and Number Theory
- Information Systems
- Computational Theory and Mathematics

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## Cite this

Burago, D., & De Rougemont, M. (1998). On the Average-Case Complexity of the Graph Reliability Problem on Gaussian Distributions.

*Fundamenta Informaticae*,*36*(4), 307-315. https://doi.org/10.3233/fi-1998-3641