Exploring Maps with Greedy Navigators

TL;DR

This paper introduces a greedy spatial navigation strategy for exploring networks, highlighting how local directional decisions can improve routing efficiency and reveal unique structural properties, moving closer to real-world navigation scenarios.

Contribution

It proposes a simple greedy navigation model that accounts for local information, modifies centrality measures accordingly, and demonstrates counterintuitive effects like edge removal improving routing.

Findings

Greedy navigators can outperform traditional shortest path strategies in certain network structures.

Removing some edges can enhance routing efficiency, similar to Braess's paradox.

The proposed navigability measure captures structural properties not evident from other metrics.

Abstract

During the last decade of network research focusing on structural and dynamical properties of networks, the role of network users has been more or less underestimated from the bird's-eye view of global perspective. In this era of global positioning system equipped smartphones, however, a user's ability to access local geometric information and find efficient pathways on networks plays a crucial role, rather than the globally optimal pathways. We present a simple greedy spatial navigation strategy as a probe to explore spatial networks. These greedy navigators use directional information in every move they take, without being trapped in a dead end based on their memory about previous routes. We suggest that the centralities measures have to be modified to incorporate the navigators' behavior, and present the intriguing effect of navigators' greediness where removing some edges may actually enhance the routing efficiency, which is reminiscent of Braess's paradox. In addition, using samples of road structures in large cities around the world, it is shown that the navigability measure we define reflects unique structural properties, which are not easy to predict from other topological characteristics. In this respect, we believe that our routing scheme significantly moves the routing problem on networks one step closer to reality, incorporating the inevitable incompleteness of navigators' information.