Abstract
Least cost paths have been used extensively in the archaeological study of ancient routeways. In this paper the principal interest is less in tracing detailed paths than in modelling long-distance travel through an extensive network over land and water. We present a novel, computationally-efficient method for avoiding the direction-dependent, positive biases in least cost paths encountered in standard algorithms. A methodology for generating networks of such paths is introduced based on a trade-off between building and travel costs, minimizing the total cost. We use the Peutinger Table, an illustrated itinerarium of the Roman empire, to calibrate the parameter controlling network complexity. The problem of how to weight land versus sea travel costs in the network is tackled by comparing itineraries of Delphic theoroi of the third century BCE with solutions of the asymmetric travelling salesman problem, a classic graph theory puzzle.