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Related Experiment Video

Updated: Jun 14, 2026

Evaluating the Effect of Roadside Parking on a Dual-Direction Urban Street

Evaluating the Effect of Roadside Parking on a Dual-Direction Urban Street

Published on: January 20, 2023

Towards design principles for optimal transport networks.

G Li¹, S D S Reis, A A Moreira

¹Center for Polymer Studies, Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA.

Physical Review Letters

|April 7, 2010

Summary

This summary is machine-generated.

We found the optimal way to navigate complex networks with limited link costs. This strategy works for both local and global navigation, unlike unconstrained networks.

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Area of Science:

Network science
Complex systems
Statistical physics

Background:

Investigating navigation in lattices with long-range connections is crucial for understanding real-world networks.
Existing models often lack cost constraints, limiting their applicability.
The U.S. airport network serves as a relevant real-world example.

Purpose of the Study:

To determine optimal navigation strategies in lattices with long-range connections under a cost constraint.
To analyze the impact of adding shortcuts with a specific probability distribution.
To compare constrained navigation with unconstrained navigation strategies.

Main Methods:

Constructing a two-dimensional square lattice with long-range connections (shortcuts).
Defining shortcut probability P(ij) proportional to r(ij)^(-alpha), where r(ij) is Manhattan distance.
Introducing a cost constraint on the total length of added links.
Analyzing optimal transport for different values of alpha and dimensions (d=1, d=2).

Main Results:

Optimal transport is achieved when alpha equals d+1 (where d is the dimension) under cost constraints.
This condition (alpha=d+1) proves optimal for both local and global navigation strategies.
This contrasts sharply with unconstrained navigation, where optimal conditions are alpha=0 (global) and alpha=d (local).

Conclusions:

The cost constraint fundamentally alters optimal network navigation strategies.
The alpha=d+1 condition provides a robust optimal transport solution for constrained networks.
Findings are validated using data from the U.S. airport network, suggesting broad applicability.