Structure, Scaling, and Phase Transition in the Optimal Transport Network

Bohn, Steffen; Magnasco, Marcelo O.

doi:10.1103/physrevlett.98.088702

Cited by 121 publications

(178 citation statements)

References 14 publications

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“…In the physical framework and the zero-temperature limit, we minimize H to obtain the ground state of the system or the optimal path configuration of the corresponding routing system. Some simple forms of H are already meaningful; for instance, ϕðxÞ = x γ , where the cases with γ > 1 penalize overlaps to suppress congestion, whereas γ < 1 encourages overlaps to aggregate traffic (28)(29)(30). The case of γ = 1 reduces to…”

Section: Modelmentioning

confidence: 99%

From the physics of interacting polymers to optimizing routes on the London Underground

Yeung

Saad

Wong

2013

Proc. Natl. Acad. Sci. U.S.A.

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Optimizing paths on networks is crucial for many applications, ranging from subway traffic to Internet communication. Because global path optimization that takes account of all path choices simultaneously is computationally hard, most existing routing algorithms optimize paths individually, thus providing suboptimal solutions. We use the physics of interacting polymers and disordered systems to analyze macroscopic properties of generic path optimization problems and derive a simple, principled, generic, and distributed routing algorithm capable of considering all individual path choices simultaneously. We demonstrate the efficacy of the algorithm by applying it to: (i) random graphs resembling Internet overlay networks, (ii) travel on the London Underground network based on Oyster card data, and (iii) the global airport network. Analytically derived macroscopic properties give rise to insightful new routing phenomena, including phase transitions and scaling laws, that facilitate better understanding of the appropriate operational regimes and their limitations, which are difficult to obtain otherwise. P ath optimization affects many of our daily activities. Although much attention has been dedicated to routing algorithms for Internet applications, such as instant messengers and peer-to-peer systems (1, 2), many other essential routing applications have attracted less attention, ranging from water distribution networks (3) to sensor networks (4), military convoy movements (5), and journey planners (6, 7). In many applications, enormous costs are incurred due to traffic congestion or nonessential and redundant capacity. Due to the computational costs involved, most existing routing algorithms are static and based on selfish decisions, with nonadaptive routing tables indicating the shortest path to destinations regardless of local traffic (8, 9). Dynamic routing protocols do exist, but they are either heuristic, probabilistic, or insensitive to other individual path decisions that dynamically constitute the traffic (10, 11). A more global approach that takes into account all individual path decisions is crucial for efficient use of overstretched infrastructure. For instance, one may suppress congestion by minimizing overlaps with other routes or decrease the number of active nodes by consolidating paths to reduce infrastructure demands or energy consumption. The latter is particularly important in the context of the Internet because it can consume up to 4% of the electricity generated (12). Future applications include individualized routing and optimal resource management of prebooked air and road traffic.The difficulty in deriving a globally optimal algorithm, in contrast to greedy local ones, lies in the simultaneous assignment of multiple interacting paths to minimize a global cost, because the optimal path between any particular source-destination pair depends on all other path choices. Such interaction is highly nonlocal, because paths between different source-destination pairs may partially overlap. Existing a...

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Section: Modelmentioning

confidence: 99%

From the physics of interacting polymers to optimizing routes on the London Underground

Yeung

Saad

Wong

2013

Proc. Natl. Acad. Sci. U.S.A.

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“…The price of additional wiring or roads is apparently offset by the ability to transport power, information, and goods to their destination in the presence of local breaks in the network (4). Furthermore, highly interconnected systems may allow a resource, like power, to be rapidly redistributed from areas with low need to those with high need.…”

mentioning

confidence: 99%

Topological basis for the robust distribution of blood to rodent neocortex

Blinder¹,

Shih²,

Rafie³

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

165

224

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The maintenance of robust blood flow to the brain is crucial to the health of brain tissue. We examined the pial network of the middle cerebral artery, which distributes blood from the cerebral arteries to the penetrating arterioles that source neocortical microvasculature, to characterize how vascular topology may support such robustness. For both mice and rats, two features dominate the topology. First, interconnected loops span the entire territory sourced by the middle cerebral artery. Although the loops comprise <10% of all branches, they maintain the overall connectivity of the network after multiple breaks. Second, >80% of offshoots from the loops are stubs that end in a single penetrating arteriole, as opposed to trees with multiple penetrating arterioles. We hypothesize that the loops and stubs protect blood flow to the parenchyma from an occlusion in a surface vessel. To test this, we assayed the viability of tissue that was sourced by an individual penetrating arteriole following occlusion of a proximal branch in the surface loop. We observed that neurons remained healthy, even when occlusion led to a reduction in the local blood flow. In contrast, direct blockage of a single penetrating arteriole invariably led to neuronal death and formation of a cyst. Our results show that the surface vasculature functions as a grid for the robust allocation of blood in the event of vascular dysfunction. The combined results of the present and prior studies imply that the pial network reallocates blood in response to changing metabolic needs.anastomoses | imaging | networks | stroke | vasculature

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“…[159] for details. Nevertheless, a nonmonotonic trend of path length as a function of the number of polymers and a phase transition at γ = 1 which resembles the transition of the flow pattern of electric currents in resistor networks [150] is observed.…”

Section: Routing As An Interaction Of Polymersmentioning

confidence: 90%

Networking—a statistical physics perspective

Yeung¹,

Saad²

2013

J. Phys. A: Math. Theor.

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Efficient networking has a substantial economic and societal impact in a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication networks become increasingly more complex, the ever increasing demand for congestion control, higher traffic capacity, quality of service, robustness and reduced energy consumption require new tools and methods to meet these conflicting requirements. The new methodology should serve for gaining better understanding of the properties of networking systems at the macroscopic level, as well as for the development of new principled optimization and management algorithms at the microscopic level. Methods of statistical physics seem best placed to provide new approaches as they have been developed specifically to deal with non-linear large scale systems. This paper aims at presenting an overview of tools and methods that have been developed within the statistical physics community and that can be readily applied to address the emerging problems in networking. These include diffusion processes, methods from disordered systems and polymer physics, probabilistic inference, which have direct relevance to network routing, file and frequency distribution, the exploration of network structures and vulnerability, and various other practical networking applications.

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Structure, Scaling, and Phase Transition in the Optimal Transport Network

Cited by 121 publications

References 14 publications

From the physics of interacting polymers to optimizing routes on the London Underground

From the physics of interacting polymers to optimizing routes on the London Underground

Topological basis for the robust distribution of blood to rodent neocortex

Networking—a statistical physics perspective

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