Jamming is limited in scale-free systems

Toroczkai, Zoltán; Bassler, Kevin E.

doi:10.1038/428716a

Cited by 211 publications

(204 citation statements)

References 4 publications

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“…We will see that even one step of such a gradient flow [5] will considerably reduce the congestion pressure in SF networks, whereas it has virtually no effect in random graphs. In addition, within the class of uncorrelated SF networks, the congestion reduction is enhanced for low (close to 2) λ values.…”

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confidence: 89%

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Using relaxational dynamics to reduce network congestion

et al. 2008

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We study the effects of relaxational dynamics on congestion pressure in scale free networks by analyzing the properties of the corresponding gradient networks [1]. Using the Family model [2] from surface-growth physics as single-step load-balancing dynamics, we show that the congestion pressure considerably drops on scale-free networks when compared with the same dynamics on random graphs. This is due to a structural transition of the corresponding gradient network clusters, which self-organize such as to reduce the congestion pressure. This reduction is enhanced when lowering the value of the connectivity exponent λ towards 2.

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confidence: 89%

“…Here, τ > 0 is the average processing time of a single packet by a node. Measuring the average fraction J = N c /N of the number of clients N c (over a period of time in the steady state), gives us a simple global measure for the congestion pressure present in the network [5]. Note that this is equivalent to J = 1 − N servers /N [5,10].…”

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Using relaxational dynamics to reduce network congestion

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“…It is interesting to notice that similar directed networks without feedback loops also emerge as gradient networks [47] and in the study of transport processes on complex networks [48].…”

Section: Optimization With Topological Constraintsmentioning

confidence: 99%

Maximum performance at minimum cost in network synchronization

Nishikawa

Motter

2006

Physica D: Nonlinear Phenomena

145

146

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We consider two optimization problems on synchronization of oscillator networks: maximization of synchronizability and minimization of synchronization cost. We first develop an extension of the well-known master stability framework to the case of non-diagonalizable Laplacian matrices. We then show that the solution sets of the two optimization problems coincide and are simultaneously characterized by a simple condition on the Laplacian eigenvalues. Among the optimal networks, we identify a subclass of hierarchical networks, characterized by the absence of feedback loops and the normalization of inputs. We show that most optimal networks are directed and non-diagonalizable, necessitating the extension of the framework. We also show how oriented spanning trees can be used to explicitly and systematically construct optimal networks under network topological constraints. Our results may provide insights into the evolutionary origin of structures in complex networks for which synchronization plays a significant role.

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“…In light of this behavior, the optimality of the shortest path routing as currently implemented has been recently questioned [6,7,8,9,10,11,12,13,14,15]. It has been shown, for example, that dynamic routing protocols which allow for a certain degree of stochasticity or take into account the congestion status of the nearest neighbors significantly improve the transport capacity of a network [9,10,11,12,13,14,15]. A more systematic approach is to find better static (strictly table-driven) routing protocols that avoid the hubs whenever possible and convenient (i.e.…”

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Optimal transport on complex networks

Danila

Marsh³

et al. 2006

Phys. Rev. E

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222

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We present a novel heuristic algorithm for routing optimization on complex networks. Previously proposed routing optimization algorithms aim at avoiding or reducing link overload. Our algorithm balances traffic on a network by minimizing the maximum node betweenness with as little path lengthening as possible, thus being useful in cases when networks are jamming due to queuing overload. By using the resulting routing table, a network can sustain significantly higher traffic without jamming than in the case of traditional shortest path routing.

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Jamming is limited in scale-free systems

Cited by 211 publications

References 4 publications

Using relaxational dynamics to reduce network congestion

Using relaxational dynamics to reduce network congestion

Maximum performance at minimum cost in network synchronization

Optimal transport on complex networks

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