### 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 |

State | Published - Dec 6 1998 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Computational Theory and Mathematics

### Cite this

**A linear time algorithm for computing the most reliable source on a series-parallel graph with unreliable edges.** / Colbourn, Charles; Xue, Guoliang.

Research output: Contribution to journal › Article

*Theoretical Computer Science*, vol. 209, no. 1-2, pp. 331-345.

}

TY - JOUR

T1 - A linear time algorithm for computing the most reliable source on a series-parallel graph with unreliable edges

AU - Colbourn, Charles

AU - Xue, Guoliang

PY - 1998/12/6

Y1 - 1998/12/6

N2 - 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(n2) 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.

AB - 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(n2) 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.

KW - Algorithms

KW - Network reliability

KW - Partial 2-trees

KW - Series-parallel graph

KW - Time complexity

UR - http://www.scopus.com/inward/record.url?scp=0346498308&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0346498308&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0346498308

VL - 209

SP - 331

EP - 345

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 1-2

ER -