### Abstract

Given a network with n vertices and m edges where each edge has an independent operational probability, we are interested in finding a vertex of the network whose expected number of reachable vertices is maximum. Such a vertex is called a most reliable source of the network. This problem was studied by Melachrinoudis and Helander (1996) where an O(n^{2}) time algorithm was proposed when the given network is a tree. In a more recent paper, Xue presented an O(n) time algorithm for this problem when the given network is a tree. In this paper, we present an O(n) time algorithm for computing the most reliable source on series-parallel graphs, using their embeddings in 2-trees.

Original language | English (US) |
---|---|

Pages (from-to) | 331-345 |

Number of pages | 15 |

Journal | Theoretical Computer Science |

Volume | 209 |

Issue number | 1-2 |

DOIs | |

State | Published - Dec 6 1998 |

Externally published | Yes |

### Keywords

- Algorithms
- Network reliability
- Partial 2-trees
- Series-parallel graph
- Time complexity

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)