Topological relationship model for geographical flows

ABSTRACT Geographical flows depict the movement of geographical objects from origin to destination. They can be applied to represent activities such as commuting, commodity trade, information exchange, and migration. The topological relationship model of geographical flows can provide information on the interactions between objects by describing whether two flows are disjoint or coincide partially or completely. For example, it can be applied to determine whether car trips within a city can be shared, identify takeout orders that can be delivered together, and prevent drone collisions. The ability to describe the topological relationship and relative direction between flows is important for analyzing the interaction between two objects. However, although many topological relationship models exist for lines, they are unable to describe both the topological relationship and the relative direction between lines accurately. To address this issue, this study developed a topological relationship model for geographical flows through the formalism of the 9-intersection model that can describe both the topological relationship and the relative direction between two flows. By removing non-existent relationships based on certain constraints, fifteen topological relationships are obtained and classified into six topological predicates. A method for determining the topological relationships was also developed that compares the section IDs and offsets of flows. The developed topological relationship model for flows was evaluated by examining a carpooling scheme based on taxi origin–destination flow data. The results show that the topological relationship model can describe the interactions among objects and select the flows that have specific interactions with other flows. A topological relationship model is proposed that describes topological relationships between flows more accurately and from more perspectives than extant models. Considering its practicability, it can be applied to alleviate various pressing issues in modern society. The model can be applied to the design of carpooling schemes to reduce carbon dioxide emissions. It can be applied to prevent drone collisions and thereby improve air transportation safety and efficiency. It can be applied to identify abnormal areas in cities to help governments better plan the layout of facilities.