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Optimal paths on the road network as directed polymers.

A P Solon1, G Bunin2, S Chu1

  • 1Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

Physical Review. E
|January 20, 2018
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Summary
This summary is machine-generated.

Optimal road paths behave like directed polymers in a disordered medium, following Kardar-Parisi-Zhang (KPZ) scaling. Network structure, particularly long-range correlations, dictates large-scale path statistics.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Understanding optimal path statistics in real-world networks is crucial.
  • Road networks exhibit complex structures influencing pathfinding.

Purpose of the Study:

  • To analyze the statistical properties of shortest and fastest paths in road networks.
  • To identify key network characteristics governing large-scale path behavior.

Main Methods:

  • Statistical analysis of road network paths between random endpoints.
  • Comparison with directed polymer models and Kardar-Parisi-Zhang (KPZ) universality class.
  • Investigation of local and large-scale network structures.

Main Results:

  • Optimal paths approximate directed polymers in a disordered medium.
  • Path statistics align with the KPZ universality class of interface roughening.
  • Large-scale path behavior is dominated by long-range network correlations, not local structure.

Conclusions:

  • Road networks share statistical similarities with disordered physical systems.
  • KPZ universality provides a framework for understanding optimal path scaling.
  • Network topology's long-range correlations are key drivers of emergent path properties.