How does the Topology of City Streets Impact on their Respective Optimization?

TL;DR

This study investigates how city street topology influences potential improvements in shortest path efficiency through added avenues, bridges, and tunnels, revealing that certain topological features significantly impact optimization gains.

Contribution

The paper introduces a method to analyze city topology effects on path optimization by deriving energy surfaces for multiple cities, highlighting the role of specific topological measures.

Findings

Energy surfaces vary significantly across cities.

Lacunarity and transitivity strongly influence path gain.

Energy surface complexity shows little correlation with topology.

Abstract

Several natural and artificial structures and systems are somehow optimized for performing specific functionalities. The structure and topology of cities is no exception, as it is critically important to ensure effective access to the several resources as well as overall mobility. The present work addresses the important subject of improving the plan of a given city through the incorporation of avenues and other express ways such as bridges and tunnels. More specifically, we start with the topology of a real city and consider the incorporation of a express way between any two locations in the city, keeping one location fixed and varying the angle of the other. The whole city area is covered in this manner, which allows us to derive a respective energy surface indicating the gain obtained regarding the average shortest path length for each of the possible situations. These surfaces therefore provide a complete picture of how much each city can be improved regarding minimal distances. Quite distinct surfaces have been obtained for 18 considered European cities. These surfaces are then characterized in terms of the number of local extrema and respective spatial complexity, expressed in terms of a raggedness measurement. Measurements are also obtained respectively to the geometry and topology of the considered cities. It is shown that the shortest path gain depends strongly on some of the considered measurements, especially lacunarity and transitivity. Interestingly, the intricacy of the energy surfaces resulted in relatively little correlation with the topological and geometrical measurements.