### Abstract

Let G = (V, E) be a (directed) graph with vertex set V and edge (arc) set E. Given a set P of (source-sink) pairs of vertices of G, an important problem that arises in the computation of network reliability is the enumeration of minimal subsets of edges (arcs) that connect/disconnect all/at least one of the given source-sink pairs of P. For undirected graphs, we show that the enumeration problems for conjunctions of paths and disjunctions of cuts can be solved in incremental polynomial time. For directed graphs both of these problems are NP-hard. We also give a polynomial delay algorithm for enumerating minimal sets of arcs connecting respectively two given nodes S_{1} and S_{2} to a given vertex t_{1}, and each vertex of a given subset of vertices T_{2}.

Original language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Editors | Jirí Fiala, Jan Kratochvíl, Vá clav Koubek |

Publisher | Springer Verlag |

Pages | 298-309 |

Number of pages | 12 |

Volume | 3153 |

ISBN (Electronic) | 3540228233, 9783540228233 |

DOIs | |

State | Published - Jan 1 2004 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 3153 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 3153, pp. 298-309). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3153). Springer Verlag. https://doi.org/10.1007/978-3-540-28629-5_21