Our knowledge of prehistoric and ancient road networks is fragmentary: Contemporary maps are rarely available and far from modern standards of precision. Some roads may be textually referenced and some are found to be still in use today while the remains of others can only be spotted from the air or sparsely sampled via ground-penetrating radar or excavation. Modern maps of ancient networks thus emerge as a conglomeration of data from many sources.
To predict missing links in incomplete networks and to better understand the principles that drive the evolution of ancient road networks, we develop and study domain-specific mathematical models.
We propose a novel model based on three simplifying assumptions concerning the growth of ancient road networks:
Our model assumes a maximal network \(G = (V, E)\) of possible road segments equipped with a terrain cost \(c \colon E \to \mathbb{R}_{> 0}\), and a set of connections \(K \subseteq \mathcal{P}_2(V)\) to establish, normally given as all pairs \(K = \mathcal{P}_2(S)\) over a set of settlements \(S \subseteq V\). If these connections are brought into an order \(\pi \in S(K)\), then a subgraph of \(G\) emerges from the following procedure, parameterized by \(\alpha \in [0, 1]\):