### Abstract

Given an unreliable communication network, we seek a most reliable source (MRS) of the network, which maximizes the expected number of nodes that are reachable from it. The problem of computing an MRS in general graphs is #P-hard. However, this problem in tree networks has been solved in a linear time. A tree network has a weakness of low capability of failure tolerance. Embedding rings into it by adding some additional certain edges to it can enhance its failure tolerance, resulting in another class of sparse networks, called the ring-tree networks. This class of network also has an underlying tree-like topology, leading to its advantage of being easily administrated. This paper concerns with an important case whose underlying topology is a strip graph, called λ-rings network, and focuses on an unreliable λ-rings network where each link has an independent operational probability while all nodes are immune to failures. We apply the Divide-and-Conquer approach to design a fast algorithm for computing an MRS, and employ a binary division tree (BDT) to analyze its time complexity to be O(||λ||2/2+[log|λ|] ||λ||1).

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

Pages (from-to) | 503-516 |

Number of pages | 14 |

Journal | Discrete Mathematics, Algorithms and Applications |

Volume | 3 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2011 |

### Fingerprint

### Keywords

- Divide-and-Conquer algorithm
- Most reliable source
- ring-tree
- underlying topology

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

### Cite this

**A divide-and-conquer algorithm for finding a most reliable source on a ring-embedded tree network with unreliable edges.** / Ding, W. E.I.; Xue, Guoliang.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - A divide-and-conquer algorithm for finding a most reliable source on a ring-embedded tree network with unreliable edges

AU - Ding, W. E.I.

AU - Xue, Guoliang

PY - 2011/12/1

Y1 - 2011/12/1

N2 - Given an unreliable communication network, we seek a most reliable source (MRS) of the network, which maximizes the expected number of nodes that are reachable from it. The problem of computing an MRS in general graphs is #P-hard. However, this problem in tree networks has been solved in a linear time. A tree network has a weakness of low capability of failure tolerance. Embedding rings into it by adding some additional certain edges to it can enhance its failure tolerance, resulting in another class of sparse networks, called the ring-tree networks. This class of network also has an underlying tree-like topology, leading to its advantage of being easily administrated. This paper concerns with an important case whose underlying topology is a strip graph, called λ-rings network, and focuses on an unreliable λ-rings network where each link has an independent operational probability while all nodes are immune to failures. We apply the Divide-and-Conquer approach to design a fast algorithm for computing an MRS, and employ a binary division tree (BDT) to analyze its time complexity to be O(||λ||2/2+[log|λ|] ||λ||1).

AB - Given an unreliable communication network, we seek a most reliable source (MRS) of the network, which maximizes the expected number of nodes that are reachable from it. The problem of computing an MRS in general graphs is #P-hard. However, this problem in tree networks has been solved in a linear time. A tree network has a weakness of low capability of failure tolerance. Embedding rings into it by adding some additional certain edges to it can enhance its failure tolerance, resulting in another class of sparse networks, called the ring-tree networks. This class of network also has an underlying tree-like topology, leading to its advantage of being easily administrated. This paper concerns with an important case whose underlying topology is a strip graph, called λ-rings network, and focuses on an unreliable λ-rings network where each link has an independent operational probability while all nodes are immune to failures. We apply the Divide-and-Conquer approach to design a fast algorithm for computing an MRS, and employ a binary division tree (BDT) to analyze its time complexity to be O(||λ||2/2+[log|λ|] ||λ||1).

KW - Divide-and-Conquer algorithm

KW - Most reliable source

KW - ring-tree

KW - underlying topology

UR - http://www.scopus.com/inward/record.url?scp=85073150217&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85073150217&partnerID=8YFLogxK

U2 - 10.1142/S1793830911001371

DO - 10.1142/S1793830911001371

M3 - Article

AN - SCOPUS:85073150217

VL - 3

SP - 503

EP - 516

JO - Discrete Mathematics, Algorithms and Applications

JF - Discrete Mathematics, Algorithms and Applications

SN - 1793-8309

IS - 4

ER -