Flooding in weighted sparse random graphs

Hamed Amini, Moez Draief, Marc Lelarge

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

In this paper, we study the impact of edge weights on distances in sparse random graphs. We interpret these weights as delays and take them as independent and identically distributed 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 standard 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 prefactor. These results 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 languageEnglish (US)
Pages (from-to)1-26
Number of pages26
JournalSIAM Journal on Discrete Mathematics
Volume27
Issue number1
DOIs
StatePublished - May 6 2013
Externally publishedYes

Keywords

  • Branching processes
  • Broadcast
  • Configuration model
  • Distances in weighted graphs
  • Flooding

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Flooding in weighted sparse random graphs'. Together they form a unique fingerprint.

Cite this