### Abstract

In this paper, we study the impact of edge weights on distances in diluted random graphs. We interpret these weights as delays, and take them as i.i.d exponential random variables. We analyze the weighted flooding time defined as the minimum time needed to reach all nodes from one uniformly chosen node, and the weighted diameter corresponding to the largest distance between any pair of vertices. Under some regularity conditions on the degree sequence of the random graph, we show that these quantities grow as the logarithm of n, when the size of the graph n tends to infinity. We also derive the exact value for the prefactors. These allow us to analyze an asynchronous randomized broadcast algorithm for random regular graphs. Our results show that the asynchronous version of the algorithm performs better than its synchronized version: in the large size limit of the graph, it will reach the whole network faster even if the local dynamics are similar on average.

Original language | English (US) |
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Title of host publication | 8th Workshop on Analytic Algorithmics and Combinatorics 2011, ANALCO 2011 |

Publisher | Society for Industrial and Applied Mathematics Publications |

Pages | 1-15 |

Number of pages | 15 |

ISBN (Print) | 9781617823152 |

State | Published - 2011 |

Externally published | Yes |

Event | 8th Workshop on Analytic Algorithmics and Combinatorics, ANALCO 2011 - San Francisco, United States Duration: Jan 22 2011 → … |

### Other

Other | 8th Workshop on Analytic Algorithmics and Combinatorics, ANALCO 2011 |
---|---|

Country | United States |

City | San Francisco |

Period | 1/22/11 → … |

### Fingerprint

### ASJC Scopus subject areas

- Applied Mathematics
- Materials Chemistry
- Discrete Mathematics and Combinatorics

### Cite this

*8th Workshop on Analytic Algorithmics and Combinatorics 2011, ANALCO 2011*(pp. 1-15). Society for Industrial and Applied Mathematics Publications.

**Flooding in weighted random graphs.** / Amini, Leo Hamed; Draief, Moez; Lelarge, Marc.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*8th Workshop on Analytic Algorithmics and Combinatorics 2011, ANALCO 2011.*Society for Industrial and Applied Mathematics Publications, pp. 1-15, 8th Workshop on Analytic Algorithmics and Combinatorics, ANALCO 2011, San Francisco, United States, 1/22/11.

}

TY - GEN

T1 - Flooding in weighted random graphs

AU - Amini, Leo Hamed

AU - Draief, Moez

AU - Lelarge, Marc

PY - 2011

Y1 - 2011

N2 - In this paper, we study the impact of edge weights on distances in diluted random graphs. We interpret these weights as delays, and take them as i.i.d exponential random variables. We analyze the weighted flooding time defined as the minimum time needed to reach all nodes from one uniformly chosen node, and the weighted diameter corresponding to the largest distance between any pair of vertices. Under some regularity conditions on the degree sequence of the random graph, we show that these quantities grow as the logarithm of n, when the size of the graph n tends to infinity. We also derive the exact value for the prefactors. These allow us to analyze an asynchronous randomized broadcast algorithm for random regular graphs. Our results show that the asynchronous version of the algorithm performs better than its synchronized version: in the large size limit of the graph, it will reach the whole network faster even if the local dynamics are similar on average.

AB - In this paper, we study the impact of edge weights on distances in diluted random graphs. We interpret these weights as delays, and take them as i.i.d exponential random variables. We analyze the weighted flooding time defined as the minimum time needed to reach all nodes from one uniformly chosen node, and the weighted diameter corresponding to the largest distance between any pair of vertices. Under some regularity conditions on the degree sequence of the random graph, we show that these quantities grow as the logarithm of n, when the size of the graph n tends to infinity. We also derive the exact value for the prefactors. These allow us to analyze an asynchronous randomized broadcast algorithm for random regular graphs. Our results show that the asynchronous version of the algorithm performs better than its synchronized version: in the large size limit of the graph, it will reach the whole network faster even if the local dynamics are similar on average.

UR - http://www.scopus.com/inward/record.url?scp=84959882296&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84959882296&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781617823152

SP - 1

EP - 15

BT - 8th Workshop on Analytic Algorithmics and Combinatorics 2011, ANALCO 2011

PB - Society for Industrial and Applied Mathematics Publications

ER -