Jamming in complex gradient networks

Park, Kwangho; Lai, Ying–Cheng; Zhao, Liang; Ye, Nong

doi:10.1103/physreve.71.065105

Cited by 62 publications

(67 citation statements)

References 11 publications

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“…Transport and flow on complex networks have also become the subject of intensive research with applications to biological, transportation, communication, and infrastructure networks [30,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63]. While our main motivation is the above described synchronization phenomena in noisy environments, we also explore some natural connections with idealized transport and flow problems on complex networks, in particular, connections with local routing schemes [55,56,59].…”

Section: Introductionmentioning

confidence: 99%

Synchronization in weighted uncorrelated complex networks in a noisy environment: Optimization and connections with transport efficiency

Korniss

2007

Phys. Rev. E

111

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Abstract. Motivated by synchronization problems in noisy environments, we study the Edwards-Wilkinson process on weighted uncorrelated scale-free networks. We consider a specific form of the weights, where the strength (and the associated cost) of a link is proportional to (k i k j ) β with k i and k j being the degrees of the nodes connected by the link. Subject to the constraint that the total network cost is fixed, we find that in the mean-field approximation on uncorrelated scale-free graphs, synchronization is optimal at β * =−1. Numerical results, based on exact numerical diagonalization of the corresponding network Laplacian, confirm the mean-field results, with small corrections to the optimal value of β * . Employing our recent connections between the Edwards-Wilkinson process and resistor networks, and some well-known connections between random walks and resistor networks, we also pursue a naturally related problem of optimizing performance in queue-limited communication networks utilizing local weighted routing schemes.

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Section: Introductionmentioning

confidence: 99%

Synchronization in weighted uncorrelated complex networks in a noisy environment: Optimization and connections with transport efficiency

Korniss

2007

Phys. Rev. E

111

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“…The quantities to be transported can either be of a material nature such as power or goods, or of a non-material nature such as information packets, which are transported on the Internet, or influence, which is transported on social networks [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]. Optimization of network transport is thus an important problem for a variety of fields in science and technology.…”

Section: Introductionmentioning

confidence: 99%

Transport optimization on complex networks

Danila

Marsh

et al. 2007

Chaos: An Interdisciplinary Journal of Nonlinear Science

101

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We present a comparative study of the application of a recently introduced heuristic algorithm to the optimization of transport on three major types of complex networks. The algorithm balances network traffic iteratively by minimizing the maximum node betweenness with as little path lengthening as possible. We show that by using this optimal routing, a network can sustain significantly higher traffic without jamming than in the case of shortest path routing. A formula is proved that allows quick computation of the average number of hops along the path and of the average travel times once the betweennesses of the nodes are computed. Using this formula, we show that routing optimization preserves the small-world character exhibited by networks under shortest path routing, and that it significantly reduces the average travel time on congested networks with only a negligible increase in the average travel time at low loads. Finally, we study the correlation between the weights of the links in the case of optimal routing and the betweennesses of the nodes connected by them.Keywords: complex networks, scaling laws, transport * dbogdan@mail.uh.edu † marshj@ainfosec.com ‡ bassler@uh.edu 1 One of the most important problems in the study of complex networks is how to best route transport on the networks. This problem is important because transport is the main function of many natural and human-made networks. Often, the transport routes used on networks are the so-called shortest-path routes, which are the routes with the minimum number of hops between any two nodes. However, this approach, which is currently used to route transport of information packets on the Internet, typically leads to congestion and eventually jamming of highly connected nodes of the networks called hubs. For this reason and in light of recent research, interest has developed in finding the routing rules that allow a given network to bear the maximum possible traffic. Specifically, the problem can be stated as follows. Given a complex network and a set of processing power and traffic demand constraints for its nodes, find the set of routing rules which allow the network to bear the highest possible amount of traffic without jamming. This problem is known to be NP -hard, meaning that the time required for the computation of an exact solution increases with the number of nodes faster than any polynomial. In this paper we argue that a heuristic transport routing optimization algorithm recently published by us achieves near-optimal transport routing in polynomial time and show this to be true for three important types of complex networks. Of course, any optimized routing when compared to shortest-path routing occurs at the expense of increasing the average number of hops between the nodes. We show that with our algorithm the average number of hops after optimization increases with the number of nodes no faster than logarithmically and that optimization significantly decreases the average travel time on congested networks.

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“…Recent research on complex networks [10,11,12] has turned to focus on dynamics on networks with applications to synchronization in natural and artificial systems [13,14,15,16,17,18], and transport phenomena [19,20,21,22]. Interesting recent studies have examined the tradeoffs between redundancy and pleiotropy [23], and centralized versus decentralized design [24], in complex networks.…”

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confidence: 99%

Scaling in small-world resistor networks

et al. 2006

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We study the effective resistance of small-world resistor networks. Utilizing recent analytic results for the propagator of the Edwards-Wilkinson process on small-world networks, we obtain the asymptotic behavior of the disorder-averaged two-point resistance in the large system-size limit. We find that the small-world structure suppresses large network resistances: both the average resistance and its standard deviation approaches a finite value in the large system-size limit for any non-zero density of random links. We also consider a scenario where the link conductance decays as a power of the length of the random links, l −α . In this case we find that the average effective system resistance diverges for any non-zero value of α.

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Jamming in complex gradient networks

Cited by 62 publications

References 11 publications

Synchronization in weighted uncorrelated complex networks in a noisy environment: Optimization and connections with transport efficiency

Synchronization in weighted uncorrelated complex networks in a noisy environment: Optimization and connections with transport efficiency

Transport optimization on complex networks

Scaling in small-world resistor networks

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