The trade-off between directness and coverage in transport network growth

Designing spatial networks, such as transport networks, commonly deals with the problem of how to best connect a set of locations through a set of links. In practice, it can be crucial to order the implementation of the links in a way that facilitates early functioning of the network during growth, like in bicycle networks. However, it is unclear how this early functional structure can be achieved by different growth processes. Here, we systematically study the growth of connected planar networks, quantifying functionality of the growing network structure. We compare random growth with various greedy and human-designed, manual growth strategies. We evaluate our results via the fundamental performance metrics of directness and coverage, finding non-trivial trade-offs between them. Manual strategies fare better than greedy strategies on both metrics, while random strategies perform worst and are unlikely to be Pareto efficient. Centrality-based greedy strategies tend to perform best for directness but are worse than random strategies for coverage, while coverage-based greedy strategies can achieve maximum global coverage as fast as possible but perform as poorly for directness as random strategies. Directness-based greedy strategies get stuck in local optimum traps. These results hold for a number of stylized urban transport network topologies. Our insights are crucial for applications where the order in which links are added to a spatial network is important, such as in urban or regional transport network design problems.