TY - GEN

T1 - Flooding in weighted random graphs

AU - Amini, Hamed

AU - Draief, Moez

AU - Lelarge, Marc

N1 - Publisher Copyright:
© Copyright (2011) by SIAM: Society for Industrial and Applied Mathematics. All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

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.

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U2 - 10.1137/1.9781611973013.1

DO - 10.1137/1.9781611973013.1

M3 - Conference contribution

AN - SCOPUS:84959882296

T3 - 8th Workshop on Analytic Algorithmics and Combinatorics 2011, ANALCO 2011

SP - 1

EP - 15

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

PB - Society for Industrial and Applied Mathematics Publications

T2 - 8th Workshop on Analytic Algorithmics and Combinatorics, ANALCO 2011

Y2 - 22 January 2011

ER -