### Abstract

Given an unreliable communication network, we seek for a node which maximizes the expected number of nodes that are reachable from it. Such a node is called a most reliable source (MRS) of the network. In communication networks, failures may occur to both links and nodes. Previous studies have considered the case where each link has an independent operational probability, while the nodes are immune to failures. In practice, however, failures may happen to the nodes as well, including both transmitting fault and receiving fault. Recently, another variant of the MRS problem is studied, where all links are immune to failures and each node has an independent transmitting probability and receiving probability, and an O(n2) time algorithm is presented for computing an MRS on tree networks with n nodes. In this paper, we present a faster algorithm for this problem, with a time complexity of O(n).

Original language | English (US) |
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Pages (from-to) | 225-232 |

Number of pages | 8 |

Journal | Theoretical Computer Science |

Volume | 412 |

Issue number | 3 |

DOIs | |

State | Published - Jan 21 2011 |

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### Keywords

- Most reliable source
- Receiving probability
- Transmitting probability

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

**A linear time algorithm for computing a most reliable source on a tree network with faulty nodes.** / Ding, Wei; Xue, Guoliang.

Research output: Contribution to journal › Article

*Theoretical Computer Science*, vol. 412, no. 3, pp. 225-232. https://doi.org/10.1016/j.tcs.2009.08.003

}

TY - JOUR

T1 - A linear time algorithm for computing a most reliable source on a tree network with faulty nodes

AU - Ding, Wei

AU - Xue, Guoliang

PY - 2011/1/21

Y1 - 2011/1/21

N2 - Given an unreliable communication network, we seek for a node which maximizes the expected number of nodes that are reachable from it. Such a node is called a most reliable source (MRS) of the network. In communication networks, failures may occur to both links and nodes. Previous studies have considered the case where each link has an independent operational probability, while the nodes are immune to failures. In practice, however, failures may happen to the nodes as well, including both transmitting fault and receiving fault. Recently, another variant of the MRS problem is studied, where all links are immune to failures and each node has an independent transmitting probability and receiving probability, and an O(n2) time algorithm is presented for computing an MRS on tree networks with n nodes. In this paper, we present a faster algorithm for this problem, with a time complexity of O(n).

AB - Given an unreliable communication network, we seek for a node which maximizes the expected number of nodes that are reachable from it. Such a node is called a most reliable source (MRS) of the network. In communication networks, failures may occur to both links and nodes. Previous studies have considered the case where each link has an independent operational probability, while the nodes are immune to failures. In practice, however, failures may happen to the nodes as well, including both transmitting fault and receiving fault. Recently, another variant of the MRS problem is studied, where all links are immune to failures and each node has an independent transmitting probability and receiving probability, and an O(n2) time algorithm is presented for computing an MRS on tree networks with n nodes. In this paper, we present a faster algorithm for this problem, with a time complexity of O(n).

KW - Most reliable source

KW - Receiving probability

KW - Transmitting probability

UR - http://www.scopus.com/inward/record.url?scp=78650587290&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650587290&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2009.08.003

DO - 10.1016/j.tcs.2009.08.003

M3 - Article

VL - 412

SP - 225

EP - 232

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 3

ER -