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On Static and Dynamic Partitioning Behavior of LargeScale P2P Networks
, 2008
"... In this paper, we analyze the problem of network disconnection in the context of largescale P2P networks and understand how both static and dynamic patterns of node failure affect the resilience of such graphs. We start by applying classical results from random graph theory to show that a large va ..."
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Cited by 15 (13 self)
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In this paper, we analyze the problem of network disconnection in the context of largescale P2P networks and understand how both static and dynamic patterns of node failure affect the resilience of such graphs. We start by applying classical results from random graph theory to show that a large variety of deterministic and random P2P graphs almost surely (i.e., with probability 1 (1)) remain connected under random failure if and only if they have no isolated nodes. This simple, yet powerful, result subsequently allows us to derive in closedform the probability that a P2P network develops isolated nodes, and therefore partitions, under both types of node failure. We finish the paper by demonstrating that our models match simulations very well and that dynamic P2P systems are extremely resilient under node churn as long as the neighbor replacement delay is much smaller than the average user lifetime.
Exponential random graphs as models of overlay networks, arXiv:0810.3173, http://eprintweb.org/S/authors/All/dr/Draief/2 (under revision
"... In this paper, we give an analytic solution for graphs with n nodes and E edges for which the P −β probability of obtaining a given graph G is µ(G) = e i=1 d2 i, wherer di is the degree of node i. We describe how this model naturally appears in the context of load balancing in communication network ..."
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In this paper, we give an analytic solution for graphs with n nodes and E edges for which the P −β probability of obtaining a given graph G is µ(G) = e i=1 d2 i, wherer di is the degree of node i. We describe how this model naturally appears in the context of load balancing in communication networks, namely PeertoPeer overlays. We then analyse the degree distribution of such graphs and show that the degrees are concentrated around their mean value. Finally, we derive asymptotic results on the number of edges crossing a graph cut and use these results (i) to compute the graph expansion and conductance, and (ii) to analyse the graph resilience to random failures. AMS classification: 60K35,60F15,68R10,90B18,05C07,05C80,05C85,05C90 Keywords: Exponential random graphs, PeertoPeer networks, overlay optimisation, load balancing,
Unstructured P2P Link Lifetimes Redux
"... Abstract—We revisit link lifetimes in random P2P graphs under dynamic node failure and create a unifying stochastic model that generalizes the majority of previous efforts in this direction. We not only allow nonexponential user lifetimes and agedependent neighbor selection, but also cover both ac ..."
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Abstract—We revisit link lifetimes in random P2P graphs under dynamic node failure and create a unifying stochastic model that generalizes the majority of previous efforts in this direction. We not only allow nonexponential user lifetimes and agedependent neighbor selection, but also cover both active and passive neighbormanagement strategies, model the lifetimes of incoming and outgoing links, derive churnrelated message volume of the system, and obtain the distribution of transient in/out degree at each user. We then discuss the impact of design parameters on overhead and resilience of the network. I.