Optimal transport on complex networks

Danila, Bogdan; Yu, Yong; Marsh, John A.; Bassler, Kevin E.

doi:10.1103/physreve.74.046106

Cited by 222 publications

(192 citation statements)

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“…Optimization of network transport is thus an important problem for a variety of fields in science and technology. In this paper we present a comparative study of the application of a recently published transport optimization algorithm [8] to three major types of complex networks: Erdős-Rényi [24], Barabási-Albert [25], and uncorrelated scale-free networks generated using the configuration model [26].…”

Section: Introductionmentioning

confidence: 99%

“…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%

“…Recently, a series of algorithms have also been proposed for network traffic optimization. These algorithms are aimed at reducing link [3,4,5,6,7] or node [8,9,10,11,12] loads by a judicious link weight assignment. They have the effect of improving network transport capacity, which is defined as the rate of particle insertion at which the network becomes jammed.…”

Section: Introductionmentioning

confidence: 99%

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Transport optimization on complex networks

Danila

Marsh

et al. 2007

Chaos: An Interdisciplinary Journal of Nonlinear Science

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Transport optimization on complex networks

Danila

Marsh

et al. 2007

Chaos: An Interdisciplinary Journal of Nonlinear Science

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101

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“…The client nodes are the ones that introduce new packets into the network, but they do not contribute to routing. Certainly, all networks will become congested at large enough driving rates γ > γ c [6]- [9], [11,12]. J indicates which network will become congested earlier, larger J meaning smaller γ c .…”

mentioning

confidence: 99%

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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“…Another algorithm called "Optimal routing" (OR) [26,27] was proposed which tries to reduce the maximum node betweenness in a self-consistent manner reaching a near-optimal configuration of paths. Good results are obtained by this algorithm despite its slow convergence.…”

Section: Introductionmentioning

confidence: 99%

Self avoiding paths routing algorithm in scale-free networks

Rachadi¹,

Jedra²,

Zahid³

2013

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this paper, we present a new routing algorithm called "the Self Avoiding Paths Routing Algorithm". Its application to traffic flow in sclae-free networks shows a great improvement over the so called "efficient routing" protocol while at the same time maintaining a relatively low average packet travel time. It has the advantage of minimizing path overlapping throughout the network in a self consistent manner with a relatively small number of iterations by maintaining an equilibrated path distribution especially among the hubs. This results in a significant shifting of the critical packet generation rate over which traffic congestion occurs, thus permitting the network to sustain more information packets in the free flow state. The performance of the algorithm is discussed both on a Barábasi-Albert (BA) network and real autonomous system (AS) network data.

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Optimal transport on complex networks

Cited by 222 publications

References 19 publications

Transport optimization on complex networks

Transport optimization on complex networks

Using relaxational dynamics to reduce network congestion

Self avoiding paths routing algorithm in scale-free networks

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