### Abstract

Given a tree network with n vertices where each edge has an operational probability, we are interested in finding a vertex on the tree whose expected number of reachable vertices is maximum. This problem was studied in Networks 27 (1996) 219-237, where an O(n^{3}) time algorithm and an O(n_{2}) time algorithm were proposed. In this paper, we present an O(n) time algorithm for the same problem, improving the previously best algorithm by a factor of O(n). We also study a max-min version of the problem and propose an O(n) time algorithm for this problem as well. Examples are provided to illustrate the algorithms.

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

Pages (from-to) | 37-45 |

Number of pages | 9 |

Journal | Networks |

Volume | 30 |

Issue number | 1 |

State | Published - Aug 1997 |

Externally published | Yes |

### Keywords

- Algorithms
- Centers
- Medians
- Network reliability
- Time complexity
- Tree networks

### ASJC Scopus subject areas

- Hardware and Architecture

### Cite this

**Linear time algorithms for computing the most reliable source on an unreliable tree network.** / Xue, Guoliang.

Research output: Contribution to journal › Article

*Networks*, vol. 30, no. 1, pp. 37-45.

}

TY - JOUR

T1 - Linear time algorithms for computing the most reliable source on an unreliable tree network

AU - Xue, Guoliang

PY - 1997/8

Y1 - 1997/8

N2 - Given a tree network with n vertices where each edge has an operational probability, we are interested in finding a vertex on the tree whose expected number of reachable vertices is maximum. This problem was studied in Networks 27 (1996) 219-237, where an O(n3) time algorithm and an O(n2) time algorithm were proposed. In this paper, we present an O(n) time algorithm for the same problem, improving the previously best algorithm by a factor of O(n). We also study a max-min version of the problem and propose an O(n) time algorithm for this problem as well. Examples are provided to illustrate the algorithms.

AB - Given a tree network with n vertices where each edge has an operational probability, we are interested in finding a vertex on the tree whose expected number of reachable vertices is maximum. This problem was studied in Networks 27 (1996) 219-237, where an O(n3) time algorithm and an O(n2) time algorithm were proposed. In this paper, we present an O(n) time algorithm for the same problem, improving the previously best algorithm by a factor of O(n). We also study a max-min version of the problem and propose an O(n) time algorithm for this problem as well. Examples are provided to illustrate the algorithms.

KW - Algorithms

KW - Centers

KW - Medians

KW - Network reliability

KW - Time complexity

KW - Tree networks

UR - http://www.scopus.com/inward/record.url?scp=0039330085&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039330085&partnerID=8YFLogxK

M3 - Article

VL - 30

SP - 37

EP - 45

JO - Networks

JF - Networks

SN - 0028-3045

IS - 1

ER -