Designing optimal transport networks

Abstract

We investigate the optimal design of networks for a general transport system. Our network is built from a regular two-dimensional ($d=2$) square lattice to be improved by adding long-range connections (shortcuts) with probability $P_{ij}\sim r_{ij}^{-\alpha }$, where $r_{ij}$ is the Euclidean distance between sites $i$ and $j$, and $\alpha$ is a variable exponent. We introduce a cost constraint on the total length of the additional links and find optimal transport in the system for $\alpha =d+1$. Remarkably, this condition remains optimal, regardless of the strategy used for navigation, being based on local or global knowledge of the network structure, in sharp contrast with the results obtained for unconstrained navigation using global or local information, where the optimal conditions are $\alpha =0$ and $\alpha =d$, respectively. The validity of our theoretical results is supported by data on the US airport network, for which $\alpha \approx 3.0$ was recently found [Bianconi {\it et al.}, arXiv:0810.4412 (2008)].

4 pages, 5 figures

References in corpus (9)

• The Price of Anarchy in Transportation Networks: Efficiency and Optimality Control
• Assessing the relevance of node features for network structure
• Optimal design of spatial distribution networks
• Structural properties of spatially embedded networks
• Extended navigability of small world networks: exact results and new insights
• Asymptotic behavior of the Kleinberg model
• Impact of community structure on information transfer
• Kleinberg Navigation in Fractal Small World Networks
• Navigating ultrasmall worlds in ultrashort time

Cited by in corpus (64)

• Spatial Networks
• Random Walks on Multiplex Networks
• A small-world of weak ties provides optimal global integration of self-similar modules in functional brain networks
• Understanding Road Usage Patterns in Urban Areas
• Enhancing network robustness for malicious attacks
• Percolation of Interdependent Networks with Inter-similarity
• Percolation of a general network of networks
• Long-Range Navigation on Complex Networks using Lévy Random Walks
• Robustness of partially interdependent network formed of clustered networks
• Breathing synchronization in interconnected networks
• Human Mobility in a Continuum Approach
• Navigable Networks as Nash Equilibria of Navigation Games
• The influence of the broadness of the degree distribution on network's robustness: comparing localized attack and random attack
• $k$-core percolation on complex networks: Comparing random, localized and targeted attacks
• The resilience of interdependent transportation networks under targeted attack
• Efficient routing on multilayered communication networks
• A model to identify urban traffic congestion hotspots in complex networks
• Suppressing traffic-driven epidemic spreading by edge-removal strategies
• Comprehensive routing strategy on multilayer networks
• Transportation dynamics on networks of mobile agents
• Enhanced Flow in Small-World Networks
• Brain modularity controls the critical behavior of spontaneous activity
• Complex networks embedded in space: Dimension and scaling relations between mass, topological distance and Euclidean distance
• Decongestion of urban areas with hotspot-pricing
• IMDB network revisited: unveiling fractal and modular properties from a typical small-world network
• Complex networks with tuneable dimensions as a universality playground
• Levy random walks on multiplex networks
• Improving information filtering via network manipulation
• Scaling properties in spatial networks and its effects on topology and traffic dynamics
• Generalized optimal paths and weight distributions revealed through the large deviations of random walks on networks
• Long-Range Connections in Transportation Networks
• Anomalous biased diffusion in networks
• Network extraction by routing optimization
• Non-Local Product Rules for Percolation
• Nonlocal PageRank
• The path most travelled: Mining road usage patterns from massive call data
• Exact Solution for Optimal Navigation with Total Cost Restriction
• Robustness of Spatial Micronetworks
• Majority-vote model on spatially embedded networks: crossover from mean-field to Ising universality classes
• A greedy-navigator approach to navigable city plans
• Fair sharing of resources in a supply network with constraints
• Critical Cooperation Range to Improve Spatial Network Robustness
• Finite-size scaling of geometric renormalization flows in complex networks
• Growing homophilic networks are natural navigable small worlds
• Two transitions in spatial modular networks
• Dynamics on Spatial Networks and the Effect of Distance Coarse Graining
• Model for the growth of the World Airline Network
• Scaling relations and finite-size scaling in gravitationally correlated lattice percolation models
• A link model approach to identify congestion hotspots
• On the decentralized navigation of multiple packages on transportation networks
• Morphological organization of point-to-point transport in complex networks
• Degree heterogeneity in spatial networks with total cost constraint
• Slow dynamics of the contact process on complex networks
• Ensemble inequivalence and absence of quasi-stationary states in long-range random networks
• Crossover from mean-field to $2d$ Directed Percolation in the contact process
• Cost of material or information flow in complex transportation networks
• Universality of critical dynamics on a complex network
• Optimal box-covering algorithm for fractal dimension of complex networks
• Navigation by anomalous random walks on complex networks
• Effects of Levy Flights Mobility Pattern on Epidemic Spreading under Limited Energy Constraint
• Identification and prioritization of urban traffic bottlenecks
• Phase Synchronization on Spacially Embeded Duplex Networks with Total Cost Constraint
• A Quality and Cost Approach for Comparison of Small-World Networks
• The conundrum of functional brain networks: small-world efficiency or fractal modularity