### 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 its 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) |
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Title of host publication | Combinatorial Optimization and Applications - 4th International Conference, COCOA 2010, Proceedings |

Pages | 268-280 |

Number of pages | 13 |

Edition | PART 2 |

DOIs | |

State | Published - Dec 1 2010 |

Event | 4th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2010 - Kailua-Kona, HI, United States Duration: Dec 18 2010 → Dec 20 2010 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Number | PART 2 |

Volume | 6509 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 4th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2010 |
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Country | United States |

City | Kailua-Kona, HI |

Period | 12/18/10 → 12/20/10 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Combinatorial Optimization and Applications - 4th International Conference, COCOA 2010, Proceedings*(PART 2 ed., pp. 268-280). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6509 LNCS, No. PART 2). https://doi.org/10.1007/978-3-642-17461-2_22